Equilibrium Breakdown and Equilibrium Selection in Evolutionary Game Theory

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

Game theory, which models decision-making by strategically interacting agents, is a basic modeling tool in economics and other social sciences. Predictions typically take the form of equilibria, which are collections of mutually optimal choices. A question that has garnered much recent attention is how agents in a repeated interaction might learn to play in accordance with equilibrium predictions. This project is a first foray into a complementary question: how play of an equilibrium may break down, to be followed by the emergence of a different equilibrium. For instance, in macroeconomic contexts, the overall state of the economy moves between booms and busts; the techniques developed in this project offer tools for understanding such transitions. Specifically, this project studies equilibrium breakdown and equilibrium selection in games played by populations of myopic agents. In our stochastic evolutionary model, agents update their strategies over time by applying noisy best response rules, under which the probability of a suboptimal choice depends on its payoff consequences. The population's aggregate behavior is described by a Markov chain on a discrete grid in the simplex. Developing methods from the theory of large deviations, we study the behavior of this process as two parameters approach their limiting values: as the noise level in agents' choice rules goes to zero, and as the size of the population goes to infinity. By taking either one of these limits, it is possible to obtain characterizations of equilibrium breakdown and selection, but these characterizations do not allow one to solve specific examples beyond the simplest cases. But we argue that taking both limits, in either order, leads to characterizations that are tractable. We conjecture that the predictions from the two orders of limits are identical, implying that the nature of equilibrium breakdown and selection does not depend on whether rarity of mistakes or the averaging effects of large numbers drives long run play.