A Framework for Modeling Population Strategies by Depth of Reasoning

This article presents a population-based cognitive hierarchy model that can be used to estimate the reasoning depth and sophistication of a collection of opponents ’ strategies from observed behavior in repeated games. This framework provides a compact representation of a distribution of com-plicated strategies by reducing them to a small number of parameters. This estimated population model can be then used to compute a best response to the observed distribu-tion over these parameters. As such, it provides a basis for building improved strategies given a history of observations of the community of agents. Results show that this model predicts and explains the winning strategies in the recent 2011 Lemonade Stand Game competition, where eight algo-rithms were pitted against each other. The Lemonade Stand Game is a three-player game with simple rules that includes both cooperative and competitive elements. Despite its ap-parent simplicity, the fact that success depends crucially on what other players do gives rise to complex interaction pat-terns, which our new framework captures well