Learning in agent based models

This paper examines the process by which agents learn to act in economic environments. Learning is particularly complicated in such situations since the environment is, at least in part, made up of other agents who are also learning. At best, one can hope to obtain analytical results for a rudimentary model. To make progress in understanding the dynamics of learning and coordination in general cases one can simulate agent based models to see whether the results obtained in skeletal models translate into the more general case. Using this approach can help us to understand which are the crucial assumptions in determining whether learning converges and, if so, to which sort of state. Three examples are presented, one in which agents learn to form trading relationships, one in which agents misspecify the model of their environment and a last one in which agents may learn to take actions which are systematically favourable, (or unfavourable) for them. In each case simulating models in which agents operate with simple rules in a complex environment, allows us to examine the role of the type of learning process used by the agents the extent to which they coordinate on a final outcome and the nature of that outcome.Learning; agent based models; simulations; equilibria; asymmetric outcomes

Walras' Unfortunate Legacy

What I argue in this paper is that the direction economics ,and particularly theoretical economics, took in the 20th century was to a great extent due to Walras' influence. This was not so much the result of his own results but rather a reflection of his vision. He was convinced that economics should have “sound mathematical foundations” and his concern for this is reflected in his correspondence with his contemporaries such as Poincaré. However, his specific vision of the nature of equilibrium became the benchmark for modern economic theory and led us to the Arrow-Debreu model which is characterised by its lack of institutional features, and the lack of any proof of stability under adjustment, as later to be shown by Sonnenschein, Mantel and Debreu. Above all there is no place in this framework for out of equilibrium dynamics. Whilst Walras is to be lauded for his insistence on the interdepence of markets, we should also be aware that he set us on a path towards economic models which, while admirably internally consistent, seem to be unable to match the empirical evidence. I fear that Walras would not have been unhappy with this outcome.Walras; mathematical foundations; equilibrium; Arrow-Debreu model; interdependence of markets

The Emergence of Coordination in Public Good Games

In physical models it is well understood that the aggregate behaviour of a system is not in one to one correspondence with the behaviour of the average individual element of that system. Yet, in many economic models the behaviour of aggregates is thought of as corresponding to that of an individual. A typical example is that of public goods experiments. A systematic feature of such experiments is that, with repetition, people contribute less to public goods. A typical explanation is that people “learn to play Nash” or something approaching it. To justify such anexplanation, an individual learning model is tested on average or aggregate data. In this paper we will examine this idea by analysing average and individual behaviour in a series of public goods experiments. We analyse data from a series of games of contributions to public goods and firstly to see what happens, if we follow the standard approach and test a learning model on the average data. We then look at individual data, examine the changes that this produces and see if somegeneral model such as the EWA (Expected Weighted Attraction) with varying parameters can account for individual behaviour. We find that once we disaggregate data such models have poor explanatory power. Groups do not learn as supposed, their behaviour differs markedly from one group to another, and the behaviour of the individuals who make up the groups also varies within groups. The decline in aggregate contributions cannot be explained by resorting to a uniformmodel of individual behaviour.Experimental Economics; Public Goods; Learning models;Individual and Aggregate behaviour.

La pensée évolutionniste dans la théorie économique néoclassique

Cette communication traite de l'utilisation des concepts évolutionnaires en économie. Une approche a été d'utiliser Vidée de révolution comme une vague analogie. Il y a deux exemples de ce type d'approche. Certains; comme Friedman, ont utilisé la notion de sélection naturelle afin de justifier le modèle standard de la théorie économique, celui d'Arrow-Debreu. D'autres ont utilisé l'idée d'évolution comme base à une critique de la nature fermée et statique de ce modèle. Une autre approche a été de prendre l'idée de l'évolution au sérieux, comme cela a été fait en théorie des jeux évolutionnaires. Je suggère que même dans ce cas, le modèle standard est incompatible avec un point de vue évolutionniste et qu'il ne suffit pas d'utiliser l'évolution comme outil pour sélectionner parmi les équilibres statiques. Des modèles économiques compatibles avec une approche évolutionnaire doivent nécessairement être très différents des modèles standards qu 'on utilise aujourd'hui.This article discusses the use of evolutionary concepts in economic theory. One approach has been to use evolution as a loose analogy. There have been two principle examples of this approach. Those such as Friedman who have used the notion of "natural selection" to justify' the standard model in economic theory, that of Arrow-Debreu and those who have used it to criticize that model for its closed and static nature. A second approach has been to take the idea of evolution more seriously as has been done in evolutionary game theory. I suggest that even in this latter case the standard model is incompatible with a truly evolutionist view and it is not enough to use evolution as a tool to select amongst static equilibria. Economic models which are consistent with an evolutionary approach have necessarily to be very different from the standard ones in use

Learning in agent based models

This paper examines the process by which agents learn to act in economic environments. Learning is particularly complicated in such situations since the environment is, at least in part, made up of other agents who are also learning. At best, one can hope to obtain analytical results for a rudimentary model. To make progress in understanding the dynamics of learning and coordination in general cases one can simulate agent based models to see whether the results obtained in skeletal models translate into the more general case. Using this approach can help us to understand which are the crucial assumptions in determining whether learning converges and, if so, to which sort of state. Three examples are presented, one in which agents learn to form trading relationships, one in which agents misspecify the model of their environment and a last one in which agents may learn to take actions which are systematically favourable, (or unfavourable) for them. In each case simulating models in which agents operate with simple rules in a complex environment, allows us to examine the role of the type of learning process used by the agents the extent to which they coordinate on a final outcome and the nature of that outcome

Walras' Unfortunate Legacy

What I argue in this paper is that the direction economics ,and particularly theoretical economics, took in the 20th century was to a great extent due to Walras' influence. This was not so much the result of his own results but rather a reflection of his vision. He was convinced that economics should have “sound mathematical foundations” and his concern for this is reflected in his correspondence with his contemporaries such as Poincaré. However, his specific vision of the nature of equilibrium became the benchmark for modern economic theory and led us to the Arrow-Debreu model which is characterised by its lack of institutional features, and the lack of any proof of stability under adjustment, as later to be shown by Sonnenschein, Mantel and Debreu. Above all there is no place in this framework for out of equilibrium dynamics. Whilst Walras is to be lauded for his insistence on the interdepence of markets, we should also be aware that he set us on a path towards economic models which, while admirably internally consistent, seem to be unable to match the empirical evidence. I fear that Walras would not have been unhappy with this outcome

Barbut, Levy, Les Marchés Efficaces et Arrow

Ce papier, préparé pour un symposium en l'honneur de Marc Barbut, discute des thèmes qui ont lié ses intérêts intellectuels et ceux de son laboratoire le CAMS aux thèmes de l'économie. En particulier il s'agit de l'historique de la notion de marchés efficaces et le refus systématique de la profession économique d'écouter les avertissements de Poincaré, Lévy, Mandelbrot et beaucoup d'autres quant à l'applicabilité de la théorie de Bachelier. Car c'est sur celle la qu'est basée la théorie moderne de la mathématique financière. Un deuxième thème concerne la structure mathématique du théorème d'impossibilité d'Arrow, des travaux de Guilbaud, le premier directeur du CAMS et Monjardet membre du CAMS, ayant largement contribué à notre compréhension de ce théorème

Born Under a Lucky Star?

This paper suggests that people can learn to behave in a way which makes them unlucky or lucky. Learning from experience will lead them to make choices which may lead to "luckier" outcomes than others. By so doing they may reinforce the choices of those who find themselves with unlucky outcomes. In this situation, people have reasonably learned to behave as they do and their behaviour is consistent with their experience. The lucky ones were not "born under a lucky star" they learned to be lucky.

Epidemics of rules, information aggregation failure and market crashes

This short paper argues that rationally motivated coordination between agents is an important ingredient to understand the current economic crisis. We argue that changes in parameters that model the structure of a macro-economy or financial markets are not exogenous but arise as agents adopt rules that appear to be the norm around them. For example, if a rule is adopted by the majority of ones' neighbors it will become acceptable or, alternatively, if agents learn that changing their rule leads to greater gains, they will modified their rules. However, as rules develop and spread they may have consequences at the aggregate level which are not anticipated by individuals. These rules may be adopted by implicit consensus as they turn out to be profitable for individuals, but they may also weaken the constraints imposed by regulators. Indeed, the emergence of new rules or the modification of old ones may render the whole system more fragile, which may then cease to function. To illustrate this we develop a simple model, motivated by the 2007-2008 crisis in credit derivatives markets, to show how coordination on simple and apparently profitable rules may cause a market to collapse.Coordination; economic crisis; economic rules; information aggregation

Changing Identity: The Emergence of Social Groups

The original Homo Economicus has progressed from an atomistic and self-interested individual to a socially embedded agent in modern economics. In particular, social interaction models suggest that the individual’s own utility of undertaking an action may be influenced by the number of peers taking this same action. Hence, people gain by conforming to, or differentiating their behaviour from that of others. A number of papers have also suggested why people want to conform. In particular, Akerlof and Kranton (2000, 2002, 2005) suggest that people belong to certain groups and wish to adopt the corresponding social identity by behaving according to the behavioural prescriptions of these groups. In this paper, we present a social interaction model that is based on a different account of identity. The concept of identity used here is on a more personal level and suggests that people have desired self-images of themselves that they wish to attain at some time in the future. Hence, individuals aim to transform their current individual characteristics into those of their self-image. They try to achieve this by joining social groups and adopting the typical characteristics of these groups. However, groups will be modified over time by the people joining them. This may induce individuals to revise their previous choices and eventually to move on and to choose different groups. The model thus presents an endogeneous interaction structure and offers an account of endogenous group formation as well as an endogenous evolution of personal identity. We further study in what sense and under what conditions the dynamics at the individual and at the social level will reach an “equilibrium” and what the nature of such an equilibrium is.Economic agent, social interaction, conformity, personal identity, self-image, change