Ianni, Antonella; (1996) Interaction patterns, learning processes and equilibria in population games. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis concerns the foundations of equilibrium notions in game theory. Game theory and its equilibrium concepts are used today as a tool for the study of many interactive environments, in particular in economics. Recent research focuses on learning processes by means of which a population of players achieves an equilibrium. This thesis contributes to this literature. The dissertation provides a general framework for the study of interacting settings that involve a finite population of players, and analyzes learning processes that sometimes lead to equilibrium. The idea is that agents learn how to face an interactive contest by reacting adaptively to their environment. In particular, we focus on a population of players, repeatedly and randomly matched to play a symmetric normal form game. We take the view that the more standard assumption of uniform random matching is not always appropriate in an economic setting. We therefore formulate a more general model, where we analyze several simple learning processes. We characterize possible equilibria at the population level, focusing on the relation between the latter and the equilibria of the underlying game. We then examine convergence properties of the processes and interpret attractors of the dynamics in terms of equilibria. In particular, the thesis analyzes the following issues: Models that depart from uniform population matching due to a highly decentralized interaction structure (i.e. locally interactive systems); Learning processes where players adopt the following boundedly rational behavioural rules: myopic best-reply, majority rules, (constant) aspiration level learning rules, payoff-independent trembles and payoff-dependent trembles. Relation between the equilibria of the population game and equilibria of the underlying game, and the effects of the interaction structure on the characterization of dynamic stability of equilibria.

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