Coordination Game Analysis using Brown’s Fictitious Play

Abstract

Coordination games prove particularly useful to analyze and model strategic interaction in a variety of fields, ranging from economics and politics to medicine, etc. Practical experimentation on coordination games points out that agents have a tendency to choose the strategy which secures a small but safe payoff rather than aim for the larger payoff and risk losing if coordination cannot be attained. This behavior can be modelled using population-based game analysis approaches, which provide guidelines for coordination expressed in terms of repetition, duration of the game and the probability of initial cooperation. In this paper, we validate these premises by employing Brown’s Fictitious Play to perform a deterministic best-response analysis of coordination games. For this purpose, we perform Matlab simulations on 2x2 games with sequential update of the best-response strategy. As such, an agent’s strategy is determined as the best-response to the observed mix of the opponent. Our simulations are performed on three instances of the coordination game: Stag Hunt, the Assurance game and the limit condition for the existence of a risk-dominated strategy.