Evolutionary Stable Solution Concepts for Initial Play

Abstract

We model initial play in bimatrix games by a large population of agents. The agents have individual solution concepts (maps from games to strategy profiles) that they use to solve games. In contrast to evolutionary game theory, where the agents play the same game indefinitely, we consider a setting where they never play the same game twice. Individual solution concepts are represented as computer programs which develop over time by a process of natural selection. We derive an aggregate solution concept (ASC), which converges to a stochastically stable state where the population mean behavior remains constant. The logic and performance of the evolutionary stable ASC is examined in detail, and its solutions to many well-known games are held up against the theoretical and empirical evidence. For example, the ASC selects the "right" solution to traveler's dilemma games, and predicts that the responder will get 40\% of the pie in ultimatum games.

Keywords: Initial play, evolutionary stability, solution concepts, strategy method

JEL Classification: C63, C73, C90