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.

The Speed of Learning in Noisy Games: Partial Reinforcement and the Sustainability of Cooperation

In an experiment, players’ ability to learn to cooperate in the repeated prisoner’s dilemma was substantially diminished when the payoffs were noisy, even though players could monitor one another's past actions perfectly. In contrast, in one-time play against a succession of opponents, noisy payoffs increased cooperation, by slowing the rate at which cooperation decays. These observations are consistent with the robust observation from the psychology literature that partial reinforcement (adding randomness to the link between an action and its consequences while holding expected payoffs constant) slows learning. This effect is magnified in the repeated game: When others are slow to learn to cooperate, the benefits of cooperation are reduced, which further hampers cooperation. These results show that a small change in the payoff environment, which changes the speed of individual learning, can have a large effect on collective behavior. And they show that there may be interesting comparative dynamics that can be derived from careful attention to the fact that at least some economic behavior is learned from experience.Economic

Evolution of Theories of Mind

This paper studies the evolution of peoples' models of how other people think -- their theories of mind. First, this is formalized within the level-k model, which postulates a hierarchy of types, such that type k plays a k times iterated best response to the uniform distribution. It is found that, under plausible conditions, lower types co-exist with higher types. The results are extended to a model of learning, in which type k plays a k times iterated best response the average of past play. The results are also extended to the cognitive hierarchy model, and to the introduction of a type that plays a Nash equilibrium.Theory of Mind; Evolution; Learning; Level-k; Fictitious Play; Cognitive Hierarchy

Cold play: Learning across bimatrix games

We study one-shot play in the set of all bimatrix games by a large population of agents. The agents never see the same game twice, but they can learn ‘across games’ by developing solution concepts that tell them how to play new games. Each agent’s individual solution concept is represented by a computer program, and natural selection is applied to derive stochastically stable solution concepts. Our aim is to develop a theory predicting how experienced agents would play in one-shot games

An Initial Implementation of the Turing Tournament to Learning in

Abstract We report on a design of a Turing tournament and its initial implementation to learning in repeated 2-person games. The principal objectives of the tournament, named after the original Turing Test, are (1) to find learning algorithms (emulators) that most closely simulate human behavior, (2) to find algorithms (detectors) that most accurately distinguish between humans and machines, and (3) to provide a demonstration of how to implement this methodology for evaluating models of human behavior. In order to test our concept, we developed the software and implemented a number of learning models well known in the literature and developed a few detectors. This initial implementation found significant differences in data generated by these learning models and humans, with the greatest ones in coordination games. Finally, we investigate the stability of our result with respect to different evaluation approaches

Three essays on behavioral game theory

176 p.Esta tesis presenta tres estudios sobre teoría de juegos del comportamiento, estudiando las desviaciones del comportamiento racional, utilizando técnicas experimentales y econométricas.El primer capítulo estudia el comportamiento en el juego del ciempiés, juego con gran interés y tradición en economía. Para ello tiene en cuenta múltiples modelos de comportamiento y gracias a un novedoso diseño intenta discernir cuál es el más relevante a la hora de explicar y predecir el comportamiento. El estudio concluye que mayoritariamente el comportamiento es explicado por el fallo del conocimiento común de la racionalidad, y que además no hay uno si no varios modelos que explican distintas proporciones de la población, lo cual explica la literatura.El segundo capítulo evalúa la capacidad predictiva de exitosos modelos de comportamiento basados en evitar el arrepentimiento. Los compara de forma teórica y en la literatura con otro modelo exitoso basado en el fallo del conocimiento común de la racionalidad, y concluye este último es el que explica mejor comportamiento atribuido originalmente a los modelos basados en arrepentimiento.El tercer capítulo compara el comportamiento en el juego del ciempiés jugando de forma simultanea o secuencial. Las diferencias se dan o no dependiendo de las características particulares del juego

Evidence based rules and learning in symmetric normal-form games

We put forth a general theory of boundedly rational behavior and learning for symmetric normal-form games with unique symmetric Nash equilibria. A class of evidence-based behavioral rules is specified, which includes best-responding to a prior and Nash play. A player begins with initial propsenities towards the rules, and given experience over time adjusts his/her propensities in proportion to the past performance of the rules. We focus on scenarios in which the past distribution of play is revealed to all players. Confronting this theory with experimental data, we find significant support for rule learning and heterogeneity among participants.Learning · rules · experimental