Economic Evolutionary Models for Finite Populations

Economic agents are often assumed to be fully rational. This assumes away bounded rationality, information problems, and computational constraints. Many economic problems can be modelled as games. The assumption of full rationality then leads to the consideration of Nash equilibria, where each agent maximizes taking the actions of other agents as given and known. Even under full rationality, though, individual actions may lead to different (strict) Nash equilibria, and some of these equilibria are more efficient than others. Even if the inherent possibility of miscoordination is assumed away, classical game theory cannot provide a prediction for such a situation: no equilibrium refinement can discard a strict equilibrium. Evolutionary Game Theory, imported from biology, studies dynamical systems where agents are boundedly rational and behavior spreads according to its perceived success. As a result, a foundation can be given for certain Nash equilibria without the assumption of full rationality; further, the theory provides equilibrium selection results in the presence of multiple equilibria. Biology, however, is concerned with large populations of randomly matched agents, while economic problems (e.g. oligopolies) typically give rise to N-player games or, more generally, finite-population frameworks. The techniques developed in biology are not well-suited for the typical economic problems. Only in recent years evolutionary concepts and techniques better suited to economics have been developed. Building on previous results by the senior applicants, this project aims to answer a series of interrelated questions within the general framework of evolutionary methods as applied to finite-population models arising from economics. Specific aims are a) the study of the evolutionary stability of perfectly competitive behavior in general frameworks; b) the incorporation of bounded memory to standard models of learning in (economic) games; c) the characterization of the relative probabilities of outcomes in applied models where more than one outcome is possible (a situation common in certain oligopoly models); d) the study of the relevance of risk-dominance and its generalizations as an evolutionary equilibrium selection criterion, specially in situations characterized by local interactions and games with more than two strategies.

The project `Economic Evolutionary Models for Finite Populations` has been a foundations project (Grundlagen) which has concentrated on mathematical-analytic techniques in order to clarify the relevance of concepts and techniques from evolutionary game theory and the theory of learning in games for the selection of Nash equilibria and, possibly, the stability of non-Nash outcomes in strategic settings relevant for Economics. In a nutshell, and in contrast with classical economic theory, in these theories economic agents are not assumed to be fully rational but rather to rely on short-sighted rules of thumb (imitation, myopic optimization). The project has concentrated on settings where the number of interacting economic agents is bounded (finite populations), as opposed to highly aggregated models typical of evolutionary game theory. The most important results (scientific advances) are as follows. First, in many economic situations, the fact that imitation is pervasive in human interactions does not always result in an inefficiency but rather creates a tendency towards more efficient outcomes. Specifically, we have proved that, when information flows appropriately, imitation favors the selection of Pareto-efficient Nash equilibria in coordination games, which are a stylized parable for economic activity. We have obtained formal results (and experimental data in the last stage of the project) showing that efficient outcomes result whenever players follow imitation rules and interaction takes place on a social network (that is, every agent interacts only with a limited number of other agents). A similar result obtains when agents are able to rely on (bounded) memory to store information from the most recent periods of interaction, which adds realism to received formal models. Second, mathematical tools have been obtained for the analysis of more realistic models of learning in games where agents might make mistakes which are sensitive to the magnitude of involved payoffs (logit response), that is, where more serious mistakes are committed less often. These models were not analytically tractable (except in some extreme cases) until now. Third, an application of the techniques to the theory of coordination of market traders on market platforms has been developed. The basic insight is that market-clearing platforms (that is, those where no price biases or rationing are implemented), which are efficient from an economic point of view, have an evolutionary advantage and will tend to survive in a large variety of markets even without public intervention. However, if market platforms (e.g. Business-To-Business, B2B) are actively designed, the designers will often find no incentive to introduce such unbiased platforms.