Coordination of agents through Learning and Evolutionary Processes : a Game Theory Approach

This article deals with the problem of agents' coordination, and with its treatment through game theory. Contrary to most works published on the subject, the emphasis is made on the process rather than on the final coordination's outcome. The problem of coordination concerns a group of individuals-or organizations-which pursue their own interests and try to establish a new and more efficient convention, i.e. a new behavioral regularity. The study of the coordination process allows us to have a better view of the different phenomena implicated in the determination of the final outcome and to understand their influence on it. Our starting point is the observation that individuals, because of their group membership, will influence each other. We shall try to show, how, in an uncertain universe, these interactions can contribute to learning on both sides, thus modifying the knowledge and then, the strategies of individuals in the emergence of an agreement. At the moment, game theory constitutes, one of the tools which is the most used in the treatment of coordination problems. Game theory deals with cases in which individuals make choices in interaction, and must be able to determine the equilibrium on which the coordination will be made. However, in many cases, it is not possible to choose one equilibrium rather than an other. It implies either to use equilibrium refinements which impose additional stability criteria to reduce the field of possible outcomes or to obtain irresolution. To study a process, we need to be within a dynamic framework, that is to postulate that individuals' choices are not simultaneous but sequential (players observe the past play before decision making). We also need to postulate incomplete information because individuals have no reason to know in every detail how the other members of the group choose their strategies. Therefore, individuals (i.e. players) have prior beliefs about the types of other players. According to the information they dispose from each play, players will have the possibility to update their expectations and beliefs. Usually, the updating process follows the Bayes rule (the Bayes rule determines the posterior probability that a player follows a particular type). This rational process of belief updating is the natural way, in game theory, to introduce a learning process. One of the main point we want to make in this article is to know if learning phenomena are limited to this unique bayesian process. To answer the question, we start by questioning Schelling's works (1986). Indeed, T. Schelling maintains that in the research process (in a tacit way) of a common solution such as the meeting point problem, « imagination often dominates reasoning and pure logic... ».[Schelling, T., 1986, p.83]. T. Schelling also emphasizes the behavior of the population as a whole, as well as the influence of population coordination on individual decision making. « The force of many social behavioral rules (...) stems from the fact that they constitute the solution of a coordination game. Everyone thinks it would be respected by others, the contrary would imply that deviant players would be pointed at by society. Fashion in clothes or also in cars arises from a process in which nobody wants to remain outside of the emerging majority and cannot go against the course of events » [Schelling, T., 1986, p.122]. For T. Schelling, learning is not exclusively produced by rational calculation, other processes seem to put pressure on the decisions of the agents. We want to know what these pressures are, where they take place, but also which models of evolution they follow. Then, we try to see if evolutionary games constitute the appropriate tool of formalization. Through this paper, we expect to go beyond the usual presentation of coordination in game theory (section 1) and to integrate learning processes (section 2) as well as the evolutionary processes 1 Faculté des Sciences Economiques-7, place Hoche-35065 RENNES CEDEX-France, Tel. 00 33 (0)2.99.25.35.33-FAX 00 33 (0)2