Origin and Recent Developments of Experimental Economics

Origin and Recent Developments of
Experimental Economics

Marco Novarese and Salvatore Rizzello^*

Università del Piemonte Orientale "Amedeo Avogadro"

1. Introduction

In the multifarious panorama of contemporary economic theory, experimental economics stands out as an especially flourishing branch, affecting all aspects of microeconomics, as well as public economics and environmental economics¹. Moreover, it is sometimes mingled with another successful branch of contemporary economics, the game theory², and, especially with reference to its latest developments, it makes use of the contributions of artificial intelligence³, of cognitive psychology⁴, of neurobiology (Hayek 1952; Rizzello 1997; Leland 1998), and of simulations with artificial agents and neural networks (connectionist approach)⁵.

In the first place, it is necessary to specify that the word experimental in economic literature is used both to define analyses in which data are gathered within a controlled artificial context, and – in its wider sense – to refer generically to an "empirical" approach to the economic science, as opposed to a deductive approach, being the former based on the use of data⁶.

This sudden and wide-ranging interest in experimentalism is quite a curious aspect in the economic science, considering that, at the beginning of this century, the unanimous approach to this discipline was aprioristic and deductive. Theories were considered empirically unverifiable, because of the impossibility to carry out experiments and collect data under the hypothesis coeteris paribus⁷.

In order to analyze the statistical data obtained from uncontrolled real contexts, econometrics was developed. In most textbooks of econometrics, economics is referred to as a science that cannot be considered experimental, since data to be used in economics cannot be collected in controlled contexts⁸. Therefore specific statistical-econometric methods become necessary.

Experimental economics and econometrics are thus often seen as incompatible disciplines⁹. Actually, this opposition is not convincing, since econometric tools are used to analyze data gathered in experimental contexts, in which there are always factors the researcher cannot control.

Yet – apart from this alleged contrast and from the role played by econometrics – after the marginalistic revolution, the aprioristic-deductive approach has been one of the unquestioned assumptions of economics, though with relevant differences. It was not typical only of the standard theory, but also of several other approaches of the 20th century. It characterized the approach of the theoreticians of equilibrium (Walras, Pareto, Arrow-Debreu) and of the theoreticians of expectations (in its wider sense, from Friedman to Lucas), as well as the approach of the founder of evolutionary economics¹⁰ (Alchian 1950), and of the Austrian school (in particular, Mises and Hayek), citing only a few examples, which often differ in crucial analytical issues¹¹.

Today one may wonder – paraphrasing a paper by Charles Plott (1990) – whether economic science is becoming an experimental science. Certainly, an answer to this question may not be based only on "quantitative" aspects (like, for instance, the exponential increase in the number of books and papers concerning experimental economics). To answer this question, one should deal with the methodological and epistemological aspects of this science, and, from this point of view, the present panorama is really very complex.

On the one hand, several scholars consider Von Mises’s approach still valid: "economics is a theoretical science and as such abstains from any judgement of value". On the other hand, Vernon Smith (1989) effectively summarizes the point of view of all those, who think that the greater part of economic theory may properly be defined an "ecclesiastic theory", which is accepted or refuted on the basis of authority, traditions or opinions concerning its assumptions, rather than because it remains valid after rigorous and repeatable falsification processes. The acknowledgement of this "epistemological handicap" is seen as the reason why, since the mid 50’s – though, as we shall see, the first experiments date back long before – a few economists have introduced laboratory experiments into their practice, in order to verify the validity of those so-called theories, which from the point of view of an experimental approach should be considered mere hypotheses.

With reference to this aspect, Hey (1991) notes that experimental economics makes it possible, first of all, to verify the intrinsic validity of a theory, by exactly respecting its conditions. Once the theory has proven intrinsically valid, its validity can be verified under less stringent conditions, and in situations which better resemble the real world.

To the questions why economists should carry out experiments, Vernon Smith gives seven answers: to test a theory or to differentiate among theories; to figure out the causes of a theory’s failure; to fix empirical regularities as a basis for new theories; to compare different environments by applying the same rule; to compare different rules in the same environment; to assess different political proposals; to use laboratories for simulating institutional plans and assessing their effectiveness¹².

As you see, wide-ranging methodological problems emerge, which cannot be dealt with in a paper whose aim is outlining a schematic (and therefore arbitrary) picture of the historical development of experimental economics. We wish to inform the reader that, from an epistemological point of view, we are venturing into a still little consolidated field, along which we will move cautiously.

We believe that, though precise and detailed answers are not available on the matter, there are clear-cut differences between experimental economics and the more traditionally experimental sciences¹³.

As a matter of fact, experimentalism seems an inevitable path for economic theory to follow, especially if the cooperation between this discipline and experimental psychology, neurobiology, and artificial intelligence keeps consolidating. Yet, several epistemological problems are still to be solved, concerning those peculiarities of social sciences (as compared to natural sciences) which are still widely debated upon by philosophers of science. From this point of view, as well, the situation is not really encouraging, since, in spite of the large number of experimental works, a solution to the above mentioned epistemological problems appears a long way off. Until a solution is found, we can only record a wide range of opinions. Nevertheless, proceeding with caution, one may note that from this variety of approaches a unitary analytical framework is emerging in experimental economics. We shall now try to list its chief elements.

Generally speaking, we can first of all say that the object of experimental economics – with the exception of the line of research in markets – is the relationship between human reasoning and decision making. One of the starting points of this literature is often the refusal of the typical hypothesis of the standard economic approach: economic agents’ perfect knowledge and substantive rationality. Though with slight differences, most hypotheses concerning individual behaviour (both tacitly assumed or explicitly stated) are consistent with the assumptions of bounded rationality, while performances are often described according to criteria of procedural rationality (Simon 1976) or strategical rationality (game theory)¹⁴. Depending on the analytical perspective, direct references to cognitive psychology and, more in general, to the results of experimental psychology, often integrate these assumptions, sometimes with complete intersections between experimental economics and experimental psychology. A melting-pot is thus created, in which typical elements of economic theory and elements of psychology of behaviour are often mingled, in order to study decision-making processes tout court (this is the case of authors such as Kahnemann, Tversky, Simon).

This aspect introduces us to the second common element in this literature: its interdisciplinarity. In experimental economics, an interdisciplinary analysis of the assumptions is now a routine procedure, with a double objective:

verify whether assumptions resemble reality,

widen the context to which the models apply.

In economic theory, such interdisciplinary approach to decision making is quite interesting and certainly innovatory, especially with reference to the analytical dimension the phenomenon is gaining. Nevertheless it cannot be considered completely new.

The relationship between economics and psychology, in particular, has been a constant characteristic of economic literature. And, in the history of economic thought, links can often be found also between economic theory and neurobiology, long before the second half of our century (Marshall 1867-8, Raffaelli 1994). Artificial intelligence has been constantly connected to economics, since the very birth of this new discipline, in the 50’s, after "cybernetics" had emerged and consolidated¹⁵.

What is quite new under the sun of contemporary literature, instead, is an overall exchange of concepts and breakthroughs between disciplines sharing the same object, i.e. explaining human decision-making processes in different contexts.

After these necessary introductory remarks, we shall now deal with the birth of experimental economics.

We distinguish four lines of research in this literature, which we do not expect to cover the subject thoroughly, being such literature so rich. We will try to illustrate what we consider the most interesting contributions. We will also deal with the present trends and in particular with one branch of experimental economics which has developed in the last decade, looking now quite fruitful. The next section illustrates the emergence and chief developments of the following lines of research:

a) experiments on individual behaviour;

b) experiments on markets;

c) experiments carried out upon and by means of the game theory;

d) experiments on individual and organizational learning.

Points a), b) and c) represent the traditional sectors of experimental economics, as we are following the widely accepted subdivision you can find in the few works on this subject. Point d) (partially overlapping in our survey point a), instead, was never introduced into historical essays, since it deals with the most recent developments. We deemed it useful to make it a separate item, to underline the fact that this is a new approach.

2. Experiments on individual behaviour and decision-making mechanisms

2.1. First experiments and methodological limits

As far as we know, the first experiment in the field was carried out by Thurstone in 1931. It was little taken into consideration, and in the surveys of the chief experiments on this subject it is often neglected. Chamberlain’s 1948 experiments (which we here mention within another line of research) is usually referred to as the first work carried out in experimental economics.

Nevertheless, Thurstone’s experiment deserves to be mentioned for several reasons. It aimed at verifying the neoclassical consumer theory, by empirically determining an individual curve of indifference. Every participant in the experiment was asked to make an hypothetical choice between baskets containing hats and shoes, hats and jackets, and shoes and jackets. For example, the participants had to choose between a basket containing 8 hats and 8 pairs of shoes and a basket containing 6 hats and 9 pairs of shoes.

Choices were hypothetical, therefore the participants in the experiments did not have to buy the preferred sets of goods.

On the basis of the data referring to one individual, the author estimated a curve of indifference (which he assumed to be hyperbola-shaped) broadly consistent with empirical observations. He concluded his work by underlining that the curves of indifference can be estimated and they adequately correspond to the results of empirical observations.

Thurstone’s work was published on the Journal of Social Psychology, not on an economic journal. As we shall discuss below, this is not a unique case, as, for a long time, important works on experimental economics were not published on economic journals, but on journals of psychology journals. The comment Milton Friedman and W. Allen Wallis (1942) made several years later on this experiment is very interesting from a methodological point of view. Their main criticism sheds light on one of the most delicate aspects of experimental economics, i.e. the presumed unreliability of its results, due to the fact that the subjects undergoing the experiments act in an artificial environment; besides – in that specific case – they made hypothetical choices¹⁶. This criticism has often been addressed to experimental economics: the participants’ motivations are not the same as those assumed in the theory.

To overcome this limit, incentives were later introduced for participants. Friedman and Sunder (1994) drew attention on the fact that such incentives should be proportioned to the participant’s performance. Yet, on this issue opinions are not unanimous: not every experimental economist considers payoffs necessary. As a matter of fact, important results were reached by means of experiments carried out without incentives (we will deal with them below)¹⁷. The second criticism has received broader consensus. It is known as the "problem of parallelism", and it refers to the artificial context in which the experiment is carried out, and to the reliability of its results outside that context¹⁸.

Experimental economists reply that, if a theory is not verified within as simple a framework as an experimental context where the subjects can earn real money, it is not likely to be verified in a real context¹⁹; moreover, excessive simplicity cannot be blamed on experimental economics, but on theories. With regard to this aspect, Hey (1991) underlines that experimental economics helps verify the intrinsic validity of a theory, by precisely respecting the assumed conditions. If that theory proves intrinsically valid, its validity can then be verified under less stringent conditions and in situations which better resemble the real world.

Going back to Thurstone’s experiment, a reply to Friedman’s and Wallis’s criticism was made by a later experiment carried out by Rousseau and Hart (1951), which was conceived as a continuation of the 1931 experiment. Also in this case the authors tried to estimate a curve of indifference, after preparing what they considered a more concrete and likely context than Thurstone’s. The subjects were asked to choose among different breakfast menus (with different quantities of eggs and bacon). Every individual had to eat the menu he had chosen, and he was not allowed to save it for future consumption. The results confirmed the outcome of Thurstone’s experiment.

In this experiment an attempt was thus made to solve the problems due to the artificial environment in which experiments were carried out; nevertheless it raised a new problem. It consists in the fact that the curves of indifference were estimated on the basis of data concerning a group of subjects, while – as is well known – according to the theory the curves of indifference are individual.

This procedure, followed also in other experiments, has given way to another front of criticism, which has often divided experimental economists themselves²⁰. Critics maintain that, in order to get reliable results in the experiments, there must be perfect correspondence between theory’s assumptions, participants’ characteristics, and the way data are collected and analyzed. Otherwise, data cannot be considered reliable.

Nevertheless, these two experiments did not receive much attention, and they are often neglected in surveys. What we call a line of research on individual behaviour and on decision-making processes is better defined and characterized by other experiments. We refer to the experiments carried out after Von Neumann’s and Morgenstern’s work Theory of Games and Economic Behaviour (1944) was published. This work laid the basis for the use of game theory within economic theory, and for the emergence of the theory of expected utility, which was to replace the traditional neoclassical consumer theory. We will go back to the game theory in the next paragraph.

2.2. The Theory of Expected Utility

In 1944 von Neumann and Morgenstern developed a normative theory of decision, according to which an action is rational if it maximizes the utility arising from the choice’s outcome. By introducing the probability method, von Neumann and Morgenstern translated the heroic assumptions of the standard theory into more realistic terms, maintaining its axiomatic method, its formal elegance, and its independence from the decision-maker’s constraints. The theory of expected utility was long considered marginal in the neoclassical theory, but it later became a fertile land and a basis for many works in experimental economics.

Along with "cognitivistic" criticisms – which underlined the lack of empirical correspondence between economic agents’ assumed capabilities and the actual human capability of acquiring and processing only a limited amount of information – other criticisms were addresses to the theory’s internal structure, and in particular to the principles of invariance, transitivity, and dominance. It is interesting to notice that such criticism grew out of a new area of research, dealing with the empirical test of a theory’s validity, by means of experimental tests.

2.2.1. Allais’s Experiments (1953)

One of the most famous violations of the theory of expected utility is the one Allais highlighted in 1953 and has since been referred to as "Allais’s paradox".

The experimental method Allais used is quite simple, and it was based on the use of hypothetical questionnaires, without the subjects receiving incentives. The subjects had to make two choices among different alternatives. The first choice to be made was between A and B, the second between C and D. Each alternative was characterized by a certain or an uncertain outcome. The outcomes of the various alternatives were the following:

alternative A	certainty to earn 100 francs
alternative B	*probability 0.1 to earn 500 francs
	*probability 0.89 to earn 100 francs
	*probability 0.01 to earn 0

alternative C	*probability 0.11 to earn 100 francs
	*probability 0.89 to earn 0
alternative D	*probability 0.1 to earn 500 francs
	*probability 0.9 to earn 0

According to the theory of expected utility, an individual who prefers A to B, will also prefer C to D.

u(x) is the utility an individual obtains from the sum x, if we assume that the alternative A is preferred to B, it follows that:

u(100)>0.1*u(500)+0.89*u(100)+0.01*u(0)
0.11*u(100)>0.1*u(500)+0.01*u(0)
If D is preferred to C, it follows that:
0.11*u(100)+0.89*u(0)<0.1*u(500)+0.9*u(0)
0.11*u(100)<0.1*u(500)+0.01*u(0)

The experiment showed that many individuals preferred A to B and D to C, thus contradicting the theory’s basic assumptions.

Allais’s experiment was repeated in more or less similar forms by other authors, obtaining equivalent results. A few of them introduced incentives in their experiments: the participants thus made real choices (with lower sums than in the original questionnaire).

2.2.2. Kahneman’s and Tversy’s Experiments

In the 70’s, Kahneman and Tversky began developing Allais’s work²¹.

Their experiments showed that individuals – unlike what is maintained in the theory of expected utility – assess probabilities and make choices under uncertainty, by means of heuristic rules implying systematic errors. Outlining the concept in brief, we may say that Kahneman and Tversky believe that human reasoning is studded with weak points; as a consequence, rationality, as defined in the maximizing approach, is characterized by an endless series of failures. This is due to our mind’s computing ability, and, above all, to biological impulses affecting decision-making processes, often by means of emotions²². One of the most famous outcomes of Kahneman’s and Tversky’s experiments is the demonstration of the invalidity of the principle of invariance (if a result is preferred to another, such order of preference cannot be modified or upset by the way in which options are confronted). Moreover, an individual’s probabilistic reasoning does not follow the rules of the theory of probability (Kahneman, Slovic and Tversky 1982)²³.

These criticism were later confirmed by several experimental sessions carried out in different contexts with different subjects (not only students, also professionals and managers)²⁴. Hypothetical questionnaires were generally used. Nevertheless, similar results were obtained introducing payoffs.

The violation of the principle of invariance was highlighted, for example, by submitting the following cases to the participants in an experiment:

Case I. Assume you are 300$ richer. You must choose between:
*assured earnings of 100$
*50% probability to win 200$ and 50% probability to win nothing

Case II. Assume you are 500$ richer. You must choose between:
*assured loss of 100$
*50% probability to lose 0 and 50% probability to lose 200$

In both cases the subjects had to choose between the certainty of owning 400$ and a lottery with equal probabilities to win 500$ and 300$. The alternatives, though, were proposed in two different ways. Such difference had a remarkable effect on preferences: while 72% of the subjects preferred the assured earnings in case I, only 36% of the same subjects chose the same alternative in case II. In case I, in the presence of possible earnings, most subjects did not want to run risks. In case II, in the presence of a possible loss, most subjects accepted to run the risk.

Kahneman and Tversky also used these results to develop a new theory consistent with empirical evidence, the Prospect Theory. It demonstrates that, in many situations, individuals are against losing a given sum more than they are attracted by earning the same sum. According to Kahneman and Tversky, those experiments demonstrate that individuals estimate little losses twice as much as earnings of the same value.

In the prospect theory the function of expected utility is replaced by a function of value. The results are weighed with decisional weights which are a function of probabilities, but are not probabilities themselves. The choices’ outcomes are assessed with reference to the status quo rather than in absolute terms. In Kahneman-Tversky’s experiments, subjects clearly showed they preferred the status quo to a lottery where they had the same probability to win 11$ or lose 10$. The lottery’s expected value is positive, and, according to the theory of expected utility, it is therefore preferred to the status quo.

The negative attitude towards losing is due to the endowment effect, as defined by Thaler (1980). This is a psychological phenomenon, driving an individual who becomes the owner of a certain good to assess it more than he did before, for the very fact of owning it²⁵.

The resulting function of value is S-shaped, and it is centred the reference point coinciding with the origin. Such function is concave for earnings and convex for losses and, it is bending more for losses than for earnings; it analytically shows that choices are influenced by the way a problem is formulated. As stated above, the outcomes change when the same problem is proposed in terms of losses or in terms of earnings.

Later, Kahneman and Tversky put forward a new version of this theory, based on new experiments. Cumulative weights are used to weigh the possible outcomes, and the original version is so applied not only to situations of risk, but also to situations of uncertainty, where two or more opposite outcomes are possible²⁶ (see also Wakker and Twersky 1993).

In the 80’s the experimental approach proves quite fruitful within the microeconomic theory of demand. Starting from the limits of the theory of expected utility, Bell (1982), Loomes and Sudgen (1982) contemporarily developed – after a series of experiments – a new alternative to the theory of expected utility, the Regret Theory. The basic idea is that when an individual has to choose between two or more alternatives, he decides not only on the basis of the concept of "acquisition of the chosen option", but also in terms of loss of the rejected alternatives. Later he might regret that choice, finding out that the outcome of the rejected alternative would have been better that the chosen alternative. In other words, a subject reasons not only in terms of earnings; he contemporarily weighs earnings and losses, the enjoyment of what he has earned and the regret for what he has lost. This regret, which the subject feels ex post, is incorporated into the individual’s function of utility²⁷.

This theory was tested with experimental data. The outcomes were mostly – yet not univocally – favourable (Loomes 1987a and 1987b).

Along with the Prospect Theory and the Regret Theory, other alternative approaches to von Neumann’s and Morgenstern’s were developed²⁸.

Some of these theories have been recently compared by Hey and Orme (1994). They estimated a series of generalizations of the theory of expected utility, among which the Prospect Theory, using experimental data on individual choice decisions. The aim was deciding whether or not one of the alternative models is to be preferred. The theory of expected utility got through this comparison, staying "intact", though the results should be read with caution, since the sample undergoing the experiment was not representative, as maintained by the authors themselves.

In other experiments John Hey, one of the most prominent experimental economists and Director of the York University Laboratory, found out that – at an aggregate level of compared statistics – the results tend to coincide with the assumptions of the theory of expected utility, despite the subjects come to a decision by means of so-called thumb rules of thumb²⁹ (Hey 1982).

Similar results were obtained in experiments on intertemporal savings and consumption: see, for instance, Hey (1987), Hey and Dardanoni (1988)³⁰.

In conclusion, we may state that the main works carried out within this line of research in experimental economics inevitably questioned – explicitly or implicitly – the hypotheses at the basis of the neoclassical theory, and in particular the theory of expected utility, as mentioned above. Though a new prevailing alternative approach has not emerged yet – as noted by Guala and Salanti (1998, p. 9) – the theoreticians of the theory of expected utility are now aware of the experiments’ results, and of the fact that such data challenge that theory.

3. Experiments on markets

An equally extensive line of research, which deals with experiments on markets, has developed along with the one concerned with individual decision-making processes. According to a widespread opinion, "experimentalism" in economics began in this sector. Edward Chamberlain’s work in 1948 is usually considered the first example of experimental economics, though, as mentioned above, it was not the first one. In that experiment transactions of a good on a competitive market were simulated, verifying prices and exchanged quantities.

Chamberlain divided his students into two groups: consumers and sellers. The structure of each student’s demand or supply (i.e., the utility of each unit bought by the consumers and the cost of each unit produced by the sellers) was indicated on a piece of paper the students received at the beginning of the experiment. The sellers earned the difference between the price at which they sold the single unit they owned and the production cost. The consumers earned the difference between the price at which they bought the good and the utility that had been attributed to that good beforehand. The cost of production and the utility of each consumer and of each buyer differed from everyone else’s. Each participant ignored the prices of the others. The market had no regulation, i.e. the students could freely move from place to place in the classroom, and they could freely negotiate with the person they chose. In the end, the total quantity of exchanged goods and the respective prices were recorded. Earnings were hypothetical, since there were no payoffs. On the basis of the reserve prices and the costs of the two groups of players, it was possible to draft the market aggregate curves of demand and supply, and to estimate the assumed equilibrium price according to the theory.

Thirty-six different combinations of curves of demand and supply were tested (by changing the combinations "cost of production/good’s utility"). The results systematically violated the theory’s conclusions, both in terms of exchanged quantities and in terms of prices.

Nevertheless, Chamberlain presented purposes and results of his experiment with caution: "The purpose of this article is to make a very tiny breach" (Chamberlain 1948, p. 95). Moreover, he did not continue this work in the following years.

His article aroused little interest until the 60’s, when these experiments were continued and developed by Vernon Smith (1962), one of Chamberlain’s students who had participated in his 1948 experiment.

Smith introduced an institutional structure for markets into these experiments, i.e. a mechanism which gathered demand and supply at each price level. It was an actual form of regulation, and its presence led to results which differed from those obtained in 1948. After a number of test sessions, during which the subjects learned the functioning of the market, exchanged quantities and prices tended to resemble the values assumed in the theory. The number of sessions that were necessary to reach an equilibrium changed according to the institutional forms. The so-called double-auction institutional form turned out to be the most efficient: subjects were allowed to put forward different demands and supplies during the same turn within a given time limit. After few test sessions, the prices and quantities obtained were closer to the equilibrium ones. Different institutional forms implied different forms of auction, characterized by alternative bid mechanisms, with the possibility to exchange larger or smaller quantities of goods.

These experiments were later extensively developed³¹, and they were applied to other market forms, such as monopoly and oligopoly. They also mingled with the game theory and its experimental analyses: a few of them are described in the next paragraph.

Along with Vernon Smith, Director of one of the chief laboratories of experimental economics at Arizona University, we can today mention Charles Plott of California Institute of Technology, and A. Roth of Harvard University.

The experiments on markets have mainly developed along a line of applied research, leaving aside the strictly theoretical aspects. For example, a few works were carried out to verify behaviours which allegedly violated antitrust rules. Others, instead, were used to test rules’ effectiveness, before making them compulsory (this kind of experiments is called testbed)³².

We would like to underline Roth’s opinion on the subject: he predicts that this sector of experimental economics will play a role in social microengineering, with the task of understanding and finding out solutions. He even foresees a new area of consulting activity in the field of institutional planning³³.

Just as chemical engineers are called upon not merely to understand the principles which govern chemical plants, but to design them [...] a measure of the success of microeconomics will be the extent to which it becomes the source of practical advice (Roth 1991, p. 113).

Nevertheless, also in this line of research, experimental works hardly influenced the prevailing theory. In experiments on markets one seldom finds detailed analyses of the implications they might have for the theory. In spite of this circumstance, this line of research has become quite relevant outside the context of economic theory, in the field of consulting activities.

4. Experiments carried out to test the Game Theory

As mentioned above, experimental economics and game theory have mingled since the very beginning³⁴. The theoreticians of game theory often deal also with experimental economics, and it is quite evident – even for those who know it only superficially – that this theory is more suited for experimental tests than other theories. In fact, in many cases a test is immediate and it seems suggested by the theory itself.

Innocenti (1995) singled out two experimental approaches which grew out of the game theory and then developed during the 50’s. The first approach was only indirectly concerned with economics, focusing its interest on psychological, social, and political aspects. The articles giving an account of these experiments were usually not published in economic journals³⁵.

Business games are the object of the second approach, in which the experimental dimension consisted in the simulation of an artificial environment, used to train and select managers. Economic theories were not questioned, they were accepted as a background for the experiments. The first business game was implemented by Richard Bellman together with other researchers, and it was presented in an article in 1957. The game simulated an oligopolist market. Each player had to run one firm. His task was fixing the selling price of a good, on the basis of the information about his own firm and the market he had at his disposal up to that moment. The game was repeated a certain number of times.

After the works carried out by Hoggatt (1959), and Siegel and Fouraker (1960), business games were used to verify theories. A prominent role in the development of this line of research was played by Rand Corporation. In 1952 in Santa Monica it promoted the seminar "The Design of Experiments in Decision Processes", and it was a reference point for chief American researchers in game theory and experimental economics.

In January 1950, at Rand Corporation, Dresher and Flood carried out an experiment introducing the game which later became known as Prisoner’s Dilemma³⁶. Two players, who could not communicate with each other, were given the following matrix:

	Column 1	Column 2
Line 1	-1, 2	0.5, 1
Line 2	0, 0.5	1, -1

In each of the 100 turns of the game, each player had to choose one line and one column respectively. Each of the four possible column/line combinations the players could choose was associated with payoffs in pennies recorded on the table. The overall sum of a win was obtained by adding the payoffs earned in each turn.

In a game of this kind, in a single context, Nash equilibrium³⁷ corresponds to the combination line 2-column 1. As regards lines, the better choice for a player is always line 2, since it guarantees the best possible result independently of the partner’s choice (0 to -1, if the choice is column 1; 1 to 0.5, if the choice is column 2). Similarly, as regards columns, column 1 is the rational choice.

Dresher and Flood reached the conclusion that the subjects tended not to behave as assumed in the theory, though they did not choose a completely cooperative behaviour. These conclusions were based on the analysis of the payoffs of a pair of players reported in Flood (1952 and 1958). In the description of this work also Nash’s opinion is reported, which differs from the authors’. Nash pointed out that the difference with the theory’s assumptions was due to a series of factors: the players interacted for 100 turns, and therefore each of them, in choosing his own strategy, had to take into account his partner’s reaction; the results would have been different, had certain conditions been different (different pairs in each turn; partner’s choice revealed only at the end of the 100 turns; unspecified number of turns).

Nash’s comment indicated a series of issues, which become central in the research of the following years. In particular, in the 80’s Axelrod studied the importance of learning in repeated games. He invited several individuals living in geographically distant places to repeat the experiment a large number of times using computer software. Unlike what happens in the Prisoner’s Dilemma (strategical competition and Nash Equilibrium), the results of Axelrod’s experiments (1984) shed light on the fact that in repeated games under uncertainty and impossibility to communicate, a cooperative behaviour emerges, with a Pareto outcome rather than Nash Equilibrium.

The Prisoner’s Dilemma was implemented in quite a wide range of experiments, carried out in different forms, in a single or a repeated context, and within different analytical frameworks. Moreover, whereas in Dresher’s and Flood’s experiments players only had to indicate the number of the line or column and the payoff matrix was asymmetrical, in later experiments symmetrical matrixes³⁸ were generally used, and games were presented in different contexts (for example, choosing whether to pollute, or whether to pay taxes)³⁹.

Siegel and Fouraker (1960) described a series of experiments carried out in the same field, which were continued in the following years. Their aim was verifying a few negotiation models (in a situation of bilateral monopoly) that had been reconsidered according to the game theory⁴⁰.

These experiments are interesting also from a methodological point of view, for a number of reasons. They were implemented very carefully and rules were described in details, unlike the first works in experimental economics⁴¹. The participants received monetary incentives and also this aspect was studied by the authors in details⁴². Siegel and Fouraker also analyzed the importance of the information the players had at their disposal: they compared situations in which the subjects only knew their own payoffs, with situations in which one subject was better informed than the other, and with contexts in which both players were fully informed⁴³. Moreover, the two authors made sure that interactions among players were anonymous, so as to avoid the introduction of uncontrolled social factors into the experiment.

In the field of game theory it is also necessary to mention Thomas Schelling’s contribution. In the 50’s and 60’s he carried out a series of experiments concerning focal points, which, among other things, supplied important methodological information concerning the experiments’ design⁴⁴.

Schelling’s experiments were based on problems of this kind:

You and your (rival) partner are to be given $100 if you can agree on how to divide it without communicating. Each of you is to write the amount of his claim on a sheet of paper; and if the two claims add to no more than $100, each gets exactly what he claimed. If the two claims exceed $100, neither of you gets anything. will receive 100$, if you can reach an agreement on how to divide them, without communicating. Each of you must write the amount he allotts to himself on a piece of paper. If the two figures give the total of 100$, each of you will receive the figure he wrote on his piece of paper, otherwise both of you will receive nothing.

You and your two (rival) partners (or rival) each have one of the letters A, B, and C. Each of you is to write these three letters A, B, C, in any order. If the order is the same on all three of your lists, you get prizes totalling $6, of which $3 goes to the one whose letter is first on all three lists, $2 to the one whose letter is second, and $1 to the person whose letter is third. If the letters are not in identical order on all three lists, non of you gets anything.are identified with the letters A, B, C respectively. Each of you must write a sequence of these three letters, without communicating with the others. If the three of you write the same sequence, the subject whose letter is the first one in the sequence will receive 6$, the subject whose letter is the second one will receive 3$, and the subject whose letter is the third one will receive 1$. If the sequences are different, the three of you receive nothing.

In the first case, subjects tended to choose 50$. This behaviour might depend upon the subject’s preference for a fair solution, or the choice of a fair division of the sum might also be due to the consideration that 50$ is a focal point, i.e. a point which is automatically evident to most individuals. Similarly, the sequence A, B, C of the second problem is a focal point. Such sequence was chosen in most cases, though the payoffs it implied were not homogeneous.

From a methodological point of view, this work showed that the data obtained and their interpretation may depend on how an experiment is designed.

Another experiment which is worth mentioning is what is known as "Ultimatum Game" (Thaler 1988). There are two players, one of them is passive, the other one is active. The active player is asked to propose the division of a given sum between himself and the passive player. If the passive player accepts that division, both of them will win the sum they agreed upon. If the passive player rejects it, both of them will win nothing. According to the theory, in this kind of situation the active player offers the least possible share of the sum to the passive player, and the passive player accepts, preferring little earnings to no earnings. Experimental tests, instead, showed that, in most cases, the active players propose fair divisions of the sum⁴⁵.

Again, it is not possible to give a complete account of the variety of experiments carried out within this line of research. As mentioned above, the experiments based on game theory might be considered as a part of one of the other categories we indicated, since game theory has been applied to different sectors of economic science. The experiments carried out within the framework of the game theory have also supplied useful results from a methodological point of view, and they are an important reference point for the other lines of research.

5. Experiments on Learning and on the Development of routines

5.1. The First Experiments

At the end of the 80’s a new line of research in experimental economics set itself the goal to analyze learning mechanisms and the development of routines at an individual and an organizational level. Though it is very recent, its origin can be traced back to that literature, emerging in the 50’s above all thanks to H. Simon’s works, in which psychology and economics are mingled. This author had supplied important contributions since the end of the 40’s (Simon 1947), the most important of which is the hypothesis of agents’ bounded rationality.

This line of research focuses its attention on the analysis of subjects’ actual computing and cognitive capabilities. Such capabilities are studied also by cognitive psychology, while they are not taken into consideration in the decision-making models of standard economics.

As research moved forward along this path, learning processes were more and more seen as one of the central issues. This means that the analysis focused on the peculiar human capability of changing one’s behaviour according to experience. Certainly, learning was already present in Von Neumann-Morgerstern’s analytical approach, where individuals’ strategical behaviour was based on their own capability of picturing the world to themselves under uncertainty (though "uncertainty" here corresponds to Knight’s risk). Yet, in this context, such analytical approach is only aimed at defining strategical rationality, and its scope is limited as compared to the work carried out by Allais’s followers.

It is now necessary to deal with the concept of learning in depth, so as to better understand this concept.

We can distinguish between associationistic learning – an aspect of the natural world, a phenomenon consisting in the association of stimuli and responses – and cognitivist learning. This second kind of learning is a different phenomenon, an active process the subject carries out to picture the external environment to himself. Such mechanism is connected with individual "cognitions" of the external world (perceptions, data interpretation, development of one’s consciousness), and it depends on how such cognitions affect actions.

The experiments carried out in this sector usually consist in a controlled situation, in which the subjects face a new problem and they must learn how to cope with it.

Several studies on decision-making processes analyzed the mechanisms of information gathering from an experimental point of view, by means of process-tracing methods. Subjects must make a choice so as to cope with a given situation, using several pieces of information. Contexts are created in which the information used by the individuals to make their choices can be observed. Data are collected on the required pieces of information, the sequence according to which they are gathered, the amount of information used, and the time necessary to use it.

A few experiments of this kind are described by Rumiati (1990), and in the mouselab software handbook of Wharton School (available on the web site http://www-marketing.wharton.upenn.edu/mouselab).

Different methods are used to collect this kind of information.

One of these methods is the protocol analysis: subjects are asked to think aloud, while they are making a choice which implies the need to search and use different pieces of information. Information is made available in different ways. It is possible, for example, to hang a number of envelopes on a showcase. Each envelop contains one piece of information. By verifying which envelopes were opened by the subject, it is possible to know which pieces of information he used.

Another possible method consists in using instruments which record eye movements, while the subject analyzes the information written on a matrix.

Another possibility is using specific computer programmes. Initially each piece of information is concealed: it is made visible when the subject carries out given actions, for example with his mouse. The display may contain the picture of a grid with a number of cells. In order to obtain one piece of information, the subject must select the cell containing it. This method of information gathering is natural for those who are familiar with PCs, and it is easy to learn by those who are not.

At any rate, the mechanism used for collecting data does notmay affect the final outcome. What does change according to the mechanism used is the time spent and the complexity of the operation. In the experiments where eye movements are recorded, information is searched and collected more rapidly and easily than in the experiments in which the pieces of information are written inside envelopes hanging on a blackboard. The possibility to look at the same piece of information more than once is of importance, in view of the limits of short-term memory. The possible distortions connected to the use of each method are not known beforehand. Subjects might use different methods to gather information in different situations. It would be therefore useful to carry out parallel experiments using different methods, in order to test the results’ reliability.

For the last few years an on-line context has been autonomously developing, in which information is selected with a mouse (like in Mouselab software): and a huge amount of information is thus available for analysis and, along with simulated ones, real consumption choices are made. The context we are talking about is the World Wide Web, which is based on hypertexts, i.e. texts in which keywords and images refer users to other pages containing further information. The development of buying and selling on line is thus creating laboratories in which choices are real. On the same site different brands of goods can be advertized, and further information concerning each good can be contained in other pages. Therefore, it is possible to know which variables the subject analyzes before choosing what to buy, and it is also possible to collect data on how consumers make their choices in real rather than experimental situations⁴⁶.

5.2. The most recent Experiments: Differentiated Learning Processes

A few laboratories have recently begun studying learning processes, assuming that they are differentiated. Such assumption is based on works concerning the application of neurobiological processes to economic theory, which were carried out for the first time by Hayek (1952).

As underlined above, in cognitivistic terms learning is connected with individual "cognitions" of the surrounding environment (perceptions, interpretations, etc.), and with the way how such cognitions determine behaviour.

Hayekx focused his attention on the process of perception of external stimuli on the part of agents, and he found out that it is subjective and idiosyncratic.

To summarize, this is how this mechanism works (please, take into account all the limits due to the necessity of summarizing)⁴⁷. The subject perceives external stimuli by means of a process, whose first result is attributing a meaning to those stimuli. They are classified by means of mental schemes, whose (genetic or social) nature is innate; yet they keep changing through experience. Our brain’s cytoarchitectonics or neural map, keeps changing its synaptic structure, and this is due to the above mentioned schemes, which either consolidate or change, according to the acquired experience.

Actions are thus the result of a rather complex process, starting from perception and subjective interpretation of external stimuli: it then continues by means of a process of endogenous development of the consciousness, essentially based on the interaction between mental schemes and experience, and it is completed by a feedback process, consisting in the application of knowledge to the environment (action). Actually, a feedback process is present in all the processes we listed, but in the first two phases it is essentially tacit and unconscious, while in the last one it might have a conscious dimension.

This is – in brief – the process we carry out when we perform an action (this is confirmed by contemporary neurobiology). If learning is linked to individual "cognitions" of the surrounding environment and to how these cognitions determine behaviour, then the fact that perceptions are differentiated, subjective, and idiosyncratic confirms the assumption of non-homogeneous learning processes. If learning processes are heterogeneous for these reasons, then we cannot give it for granted that it is possible to predetermine the outcome of repeated games, as happens, for example, in Axelrod.

Another relevant aspect emerging from this literature (see Rizzello 1997) is the path-dependent nature of neurobiological processes and the connection between perception and learning.

This brings us to a new hypothesis to be verified empirically: when a context is characterized by structural and procedural uncertainty which can be easily traced back to already experimented situations, we expect path-dependent dynamics to prevail. In other words, we believe that path-dependence plays a role in decision-making processes.

In this framework Cohen and Bacdayan (1991) performed an experiment which later Egidi and Narduzzo developed further. It analyzed learning in cooperative contexts by means of the "Target the Two" game. This is a card game in which two individuals must cooperate to achieve a common end without communicating. That end can be achieved with a number of moves that is not fixed beforehand, hence it can be achieved more or less efficiently.

While carrying out his experiment, Cohen filmed the participants. In Trento a specific software was developed in order to carry out the experiment by means of a PC network.

Nowadays several experiments are computer-assisted. Special programming languages have been developed to help researchers to obtain the software they need for their experiments⁴⁸.

Using a computer makes it possible to carry out new experiments and to redesign already known ones, since it allows to collect data which could not be otherwise stored. Nevertheless, it also gives rise to new problems that are often due to the fact that it is necessary to have a well-equipped laboratory available, and, above all, it is necessary to have advanced skills in computer science.

An extremely important (though often neglected by experimental economists) methodological problem, which we can only mention here, concerns the neutrality of this tool. This means that the fact of interacting with a computer might change participants’ behaviour, driving them to make different choices as compared to non-electronic contexts.

The laboratories we mentioned work actively to make their results known through the web. Besides, a series of experiments implemented on the web can be directly carried out by internet users. The purpose of these experiments is either didactic and explanatory, or it consists in analyzing web’s potentialities as a data-collecting tool⁴⁹, or in collecting data and carrying out research⁵⁰. Sometimes a number of subjects participate contemporarily in these experiments, and their behaviour is repeatedly compared.

With reference to this line of research, an important aspect is to be noticed: experimental economics is a fundamental tool for collecting empirical evidence on individual and collective learning processes. Collecting fieldempirical data poses, in turn, serious problems: thus, the development of new methodological analytical tools becomes necessary (on this subject, see Simon 1999).

6. Concluding remarks

On the basis of the multifarious picture emerging from this paper, we believe we can maintain that experimental economics is a vast and heterogeneous melting-pot, rather than a unitary doctrine. Despite several epistemological and methodological knotty problems are still unsolved – and some of them have not even been adequately tackled – for the last decade a more clear definition of the role and method of experimental economics has been taking shape.

Decades have passed since the first naive experimental approaches emerged; the gradual cooperation with psychologists and experts in artificial intelligence has given an important contribution to economic science, especially with reference to the necessary rigour in the pursuit of results. At the beginning, these approaches tended to indulge in verificationism, in falsificationism, in detailed descriptions, etc. Instead, the role experimental economics is apparently playing today is what Arrow defined "nano-economics", a level of analysis in which it is possible to integrate economic theory and a few results of cognitive sciences. This level of analysis – dealing with individual decision-making processes from the point of view of mental and neurobiological processes – has led to important results, for example, in the projects of research on institutional economics.

If we want to continue in this direction, it is necessary to go back over the mechanisms of a black box, whose mechanisms we thought to know, i.e. human mind. This will only be possible if psychologists, economists, experts in artificial intelligence, and neurobiologists decide to work together on a common project of research, aimed at explaining the complex decision-making phenomenon, from the point of view of mental processes.

Nowadays experts in these heterogeneous disciplines start working together in laboratories, and conditions seem more favourable. This is often due to acts of great humility, an essential prerequisite for any really interdisciplinary approach.

Today nobody knows whether or not this is the right way to go for achieving the desired results; it certainly seems still long and difficult. In a few decades we will be able to write its history.

Notes

^* Laboratorio di Economia Cognitiva, Facoltà di Giurisprudenza, C.so Borsalino, 15100 Alessandria. Novarese@cisi.unito.it, salvatore.rizzello@unito.it.

¹ See the recent Handbook of Experimental Economics by Kagel and Roth (1995), and, with reference to the connection with environmental economics, see the works carried out in the Environmental and Experimental Economics Research Laboratory of Georgia State University in Atlanta (http://prcweb.gsu.edu/enveco/enveco.html).

2 As is well known, the game theory (von Neumann and Morgerstern 1944) is a branch of mathematic analysis which studies decision-making processes in situations of strategical interaction. A situation of this kind occurs when two or more decision-makers with different aims act within the same system or share the same resources. In 1950, Dresher and Flood began the experiments which led to the famous Prisoner’s Dilemma (Flood 1952; 1958; Kalish, Milnor, Nash and Nering 1954; Shelling 1957). After that beginning, this literature has become one of the most relevant phenomena of contemporary economic theory.

3 The connection with this discipline is not only instrumental (using software as an "instrument" for carrying out experiments); artificial intelligence is used to study "human brain’s syntax" applied to decision making, or to study the emergence of behavioural rules and multiple equilibria by means of simulations with artificial agents and neural networks (see below the reference to the connectionist line of research, Terna 1992 and 1995).

4 Around the 50’s several disciplines converged, thus creating what is called "the new science of the mind". A central point in this process of integration is the development in cybernetics of the concept of feedback and its application in psychology, which brought about the abandonment of behaviourism in favour of cognitivism. Behaviourism upheld the necessity of a totally objective psychology, dealing with behavioural acts, which can be described in terms of stimulus-response; the subject does not act on the basis of his own ideas or purposes, but according to environmental stimuli.

According to cognitivism, every individual is endowed with cognitive functions allowing him to interact with his environment. Not only does an organism adjust itself to the environment, it also modifies that environment according to its needs. Attention is focused on the processes of information gathering by means of perception, subjective reorganization, and interpretation of the surrounding world. The subject is active and, from time to time, he changes his own behaviour on the basis of the information he receives from outside (Gardner 1985).

5 In the second half of the 80’s the connectionist paradigm began emerging. Unlike cognitivism, which is rooted in human sciences and is not concerned with physical-biological elements, connectionism is very interested in the elementary mind activities and in artificial intelligence. In the latter approach the attention is focused on the system’s dynamic development and, as a consequence, on the network connecting subjects, rather than on subjects themselves (Parisi 1991). In its latest advances, the connectionist approach aims at creating behavioural models simulating, by means of artificial agents, the emergence and development of complex adjusting systems. In this approach the development of specific software is crucial.

Nevertheless, the extended use of artificial intelligence for computer simulation raised criticism. According to Friedman and Sunder (1994, p. 5) for example, simulations do not supply empirical data, and cannot be considered actual experiments. They should be considered on a level with theoretical results.

6 Consider the following statement: "Pareto always expressed his definitely positivist point of view in favour of an experimental social science" (Salanti 1997, p. 6, our italics), referring to the fact that, according to Pareto, science should not be merely deductive. Certainly, Pareto did not deem it possible to carry out social experiments.

The expression experimental economics is also used to define "social experiments". One of the most famous social experiments was carried out in the 60’s in the United States, by introducing an income negative tax for given groups of individuals. Their behaviour, in terms of job supply, was analyzed for three years and compared with the behaviour of a control group. See Neuberg (1989).

7 This idea can be found also in the still most widespread textbook of economics. Samuelson and Nordhaus (1985) summarize their opinion on this aspect as follows:

One possible way of figuring out economic laws [...] is by controlled experiments [...] Economists [...] cannot perform the controlled experiments of chemists or biologists because they cannot easily control other important factors. Like astronomers or meteorologists, they must be content largely to observe." (ibid., p. 8)

8 Consider for example the following statement:

Economic theory through a formal deductive system, provides the basis for experimental abstraction and the experimental design, but society in most cases carries out the experiment, possibly using its own desing (Judge et al 1980, p. 4).

9 See, for example, Hey (1991).

10 This is one of the successful lines of research in contemporary economics - whose chief representatives are Nelson and Winter - in which the concept of natural selection is applied to firms’ behaviour on the market. The evolution due to natural selection is presented as a kind of "organizational genetics", according to which each organization adopts survival strategies based on a subjective selection of the information received from the surrounding environment.

11 Assumptions and characteristics of the aprioristic-deductive approach of economic science were made systematically explicit, as is well known, by one of Jevons’ and Wicksteed’s followers, Robbins (1932), and they were further developed and generalized by Milton Friedman (1953).

12 Along with Smith, other authors indicated new possible objectives of the use of experiments in economics. Friedman and Sunder (1994), for example, maintain that the experiments’ aim is also that of influencing the decisions of public bodies. Roth (1987) calls this practice "whispering in the ears of princes". An example is the experiment which was commissioned by the Federal Trade Commission to Grether and Plott (1984), to analyze the alleged dishonest behaviour of a monopolist firm in the energy sector.

Another example is Rassenti, McCabe and V. Smith (1994).

Finally, a few experiments were initially carried out with a pedagogical aim, as a didactic aid for teaching economic theory. Chamberlain’s pioneer work - which we will discuss below - was carried out in university classes as a didactic aid, and this is not a unique example. Bergstrom and Miller (1997) illustrate a series of experiments which were designed to explain how competitive markets work, and to show the effects of prohibition, adverse selection, etc. More examples can be found in Walls (1991) or in the Newsletter Expernomics (http://www.marietta.edu/delemeeg/ expernom).

13 To tell the truth, a few authors think that the experimental method of natural sciences is to be applied tout court to economic science.

This experimental way constitutes, of course, the prevailing methodology in many of the hard sciences; physics, chemistry and biology all consistently use the experimental approach. For such sciences, experimental tests of theories are crucially important; only by subjecting a theory to test under the same controlled conditions as those under which the theory itself was generated can a theory be properly tested. The same logic should apply in economics, especially if economists continue to borrow other aspects of the methodology of the hard sciences (Hey 1991, p. 9).

[...] without the aid of experiments [...] knowledge of electricity and magnetism would have accumulated much more slowly. Yet, in economics, "basic science" is done disproportionately by theorists, who must rely for their empirical bearings on data collected for more immediately practical purposes (Roth 1991, p. 107).

14 After introducing the concept of bounded rationality into decision-making processes, from the end of 40’s Simon (1947) has shed light on computing and cognitive limits, and he has later developed the concept of procedural rationality, working out models of problem solving and decision making that are coherent with the attainments of cognitive psychology. By means of these models, it is possible to analyze how individuals solve their problems, through heuristics. Moreover, procedural rationality becomes a central concept to understand the internal dynamics of organizations: these are seen as bodies in which problems are solved by sharing out competencies (which derives from sharing out knowledge) and developing routines.

Strategical rationality grew out of game theory, and - as we shall better see below - it is typical of the behaviour of an individual, who is in a situation of uncertainty and knows that the outcome of his choice depends also on the behaviour of one or more other individuals.

15 The word "cybernetics" was introduced by N. Wiener, who in 1948 published Cybernetics. This word derives from a Greek word meaning "steersman". It indicates a theory of self-regulating systems that applies both to machines and to living beings.

16 "It is questionable whether a subject in so artificial an experimental situation could know what choices he would make in an economic situation" (Friedman and Wallis 1942, p. 179).

17 As regards incentives in experiments on individual behaviour, Kahnemann and Tversky, two chief experimental economists, write:

[...] we maintain that monetary incentives are neither necessary nor sufficient to ensure subjects’ cooperativeness, thoughtfulness, or truthfulness. The similarity between the results obtained with and without monetary incentives in choice between simple prospects provides no special reason for skepticism about experiments without contingent payment (Kahnemann and Tversky 1992, p. 320).

An opposite opinion is, for example, Binmore’s (1994): "no credence whatsoever should be accorded to experiments in which the subjects’ performance is not rewarded with proper regard to their opportunity costs".

18 See, for example:

[...] the evidence emerging from controlled experiments carried out with students [...] may not apply to the areas of economic decision assumed in the theory. The same is true for Allais’s "examples of the armchair" (Gravelle and Rees 1981, p. 622).

19 This kind of consideration can be found in all experimental economics handbooks. Plot in his web page notices, for example, that: "Models, general theories, and principles that are unable to explain the simple and special cases of a phenomenon created in laboratory are not good candidates for application in the complex cases found in the field".

20 With reference to this debate, see for instance Roth (1993).

21 See, in particular, Kahneman and Tversky (1979).

22 One of the most famous outcomes of Kahneman-Tversky’s experiments is the demonstration of the invalidity of the principle of procedure invariance. According to this principle, if a result is preferred to another, such order of preference cannot be modified or upset by the way in which options are confronted. This aspect seems linked to Damasio’s neurobiological studies. Antonio Damasio, one of the most prominent contemporary neurologists and author of Descartes’ error (Damasio 1995), draws an intimate connection between emotion and cognition in practical decision making (due to "somatic markers"). Damasio has reached extremely interesting results starting from the distinction between pure and practical reason. His empirical works seem to confirm, at the neurobiological level, the idea that failures of traditional rationality are linked to the emotional dimension (ibidem).

23 These studies are also at the basis of a new approach in teaching statistics. See, for example, Konold (1995) and Garfield (1995).

24 Often, for convenience, students are used as subjects for experiments. Also this practice gave rise to criticism of experimental economics. Consider, for example, experiments simulating firms’ behaviour on the market (such experiments are dealt with in the next paragraph). Those who criticize experimental economics underlined that firms are not run by young students, but by expert managers; therefore the results can hardly be considered relevant. For this reason a few experiments were carried out with managers. Sometimes the differences were not remarkable. Other times they were relevant, since managers tended to act on the basis of their own knowledge and habits, and did not comply with the conditions of neutrality required in the experiments, showing path-dependent dynamics (see below). With reference to these aspects, see Friedman and Sunder (1994, p. 40) and Davis and Holt (1993, p. 17).

25 With reference to the endowment effect, see also Kahneman, Knetsch and Thaler (1990).

26 The distinction between risk and uncertainty was first introduced by Knight (1921, p. 19) there is a fundamental difference between a specified uncertainty or risk and an unspecified and immeasurable one. Uncertainty may be defined as the lack of information on the objective probability of relevant future events in the moment when economic agents must make choices. On the contrary, a situation is characterized by risk when: i) assuming that the possible states of the world do not exclude each other, every single decision is associated with a number of consequences, each of them corresponding to the accomplishment of a specific state of the world; ii) an economic agent assesses the probability of the accomplishment of the possible states of the world.

The prospect theory can also apply to situations of uncertainty by replacing the probabilities associated to each event with decisional weights.

27 We shall try to illustrate this concept with a little example by Butler and Hey (1987).

A man in a restaurant studies the menu, and after due deliberation is unsure whether to choose lemon sole or fillet steak. Finally, he decides to go for the lemon sole. When the waiter arrives to take his order, he informs the man that roast chicken, not mentioned on the menu, is also available. "In that case" replies the man, "I’ll have the steak" (p. 162).

Had this individual definitely preferred the sole, he would have confirmed his choice. On the contrary, as his behaviour, i.e. choosing the sole, was the result of assessments of the "regret" kind, his assessment structure has been altered by the introduction of a new alternative.

28 References can be found in Hey (1991), Camerer (1989), and Machina (1989).

29 This expression means: easy-to-apply decision-making rules, which do not necessarily guarantee the best possible choice.

30 There are other experiments connected to this line of research and the following one. They were performed within marketing studies, in order to analyze consumers’ behaviour; their aims - at least in principle - differ from the ones of experimental economics. Nevertheless, methods and a few theoretical references are quite similar. These experiments have practical aims, such as verifying the variables consumers use in their decision-making processes, or understanding on which basis two different brands of similar goods are compared. In this connection see, for example, Dalli and Tedeschi (1997). A few marketing experiments were described also by Rumiati (1990). For the last few years also selling on line has been studied. With reference to this, see site http://www-marketing.wharton.upenn.edu.

31 For a survey of the results of these experiments, see Davis and Holt (1993) The double-auction mechanism is quite similar to the one really used in a few share markets. The similarity increased after personal computers were introduced into this kind of experiments. Experiments were carried out in which the agents worked in a series of markets contemporarily. The double-auction mechanism has become a reference point in the assessment of the efficiency of other markets.

32 See, for instance, Plott (1996) A few testbed experiments are described on the web site of Arizona University, where Smith works: http://www.econlab.arizona.edu. One of the described experiments, for example was carried out to assess the effect of deregulation on the electric energy market. These experiments also have didactic and explanatory applications. Other examples can be found in the above mentioned Plott’s page at California Institute of Technology: http://www. hss.caltech.edu/SSGrad/plott.html.

33 http://www.economics.harvard.edu/_-alroth/alroth.html

34 As regards this aspect, see Innocenti (1995) and Roth (1993).

35 Economists themselves, as mentioned above, could not publish their first articles on experimental economics in journals of economics:

When I began my own experimental work about a dozen years ago, it was most convenient to publish the results in journals of psychology and business (Roth 1987, p. 1).

With reference to the role played by economics in the development of experimental methods in social disciplines, it is interesting to take also Simon’s opinion into account:

I do not think that impetus for experimentation within a game-theoretical framework initially came from economists, but rather from psychologists [...] statisticians and interdisciplinary types close to cybernetics and management science (Simon, in Smith 1992, pp. 253-254).

36 The famous story associated with this game was developed by A.W. Tucker. Publication of Tucker’s (1950) memo occurred in 1980. The 1950 experiment of Dresher and Flood was reported in Flood (1952; 1958).

37 As is well known, in game theory Nash Equilibrium (after the name of the mathematician and Nobel Prize winner John Nash) is a situation in which the existent set of strategies and correspondent payoffs is such that no player can improve his position by changing his strategy, without the others changing their own.

38 In symmetrical matrixes equal payoffs corresponded to equal outcomes.

39 See, for example, Kagel and Roth (1995).

40 The connection with the experiments on markets we have dealt with above is especially evident in these experiments.

41 In 1991 "Econometrica" introduced a series of requirements which experimental works must meet to be considered for publishing. Experiments must be described in details, specifying, for instance, what kind of subjects participate in the experiment, whether or not they receive incentives, number of participants, and number of turns if any, etc.

42 When the difference between the payoffs received in the optimum situation and the payoffs received in the situations close to that optimum was not remarkable, the subjects gave up negotiating before they reached the point of maximum efficiency.

43 The more the players were informed, the more they tended to establish steady collusive agreements.

44 See, for example, Schelling (1957; 1958 and 1960).

45 Cassone (1997) tries to reconcile theory and empirical evidence.

46 For considerations on this subject, see, for instance, the internet site: http://www.marketing. wharton.upenn.edu/ecommerce/Columbia%20choice%20conference%20paper1.htm

47 For a more systematic description, see Rizzello (1997).

48 See, for example, Mouselab (http://www-marketing.wharton.upenn.edu/-mouselab); TOFFEE, an instrument used to generate applications for carrying out experiments, which is being developed in Trento (http://silver.gelso.unitn.it/-miky/presentazione/node1.html); and Ratimage of Bonn University (http://www.econ1.uni-bonn.de/ratimage). At the site http://www.econlab.arizona.edu/ /eslsoft.html of Arizona laboratory, you can find the necessary programmes to carry out a series of experiments that have already been repeatedly tested.

49 See, for example: http://zia.hss.cmu.edu/miller/eep/exp1.test and http://www.elsa.berkeley. edu/vlab/expintro.html

50 On line experiments can be found at the sites: http://market.econ.vanderbilt.edu/ /monopoly. read.html and http://indiana.polito.it:10500/-nachera/Intro1.html

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