Robustness of fictitious play in a resource allocation game

Abstract

Nowadays it is well known that decentralised optimisation tasks can be represented as so-called “potential games”. An example of a resource allocation problem that can be cast as a game is the “vehicle-target assignment problem” originally proposed by Marden et al. In this article we use fictitious play as “negotiation” mechanism between the agents, and we examine its robustness in the case where a fraction of non-cooperative players, s, choose a random action. This addresses situations in which there is, e.g., a malfunction of some units. In our simulations we consider cases where the non-cooperative agents communicate their proposed action to the other agents and cases in which they do not announce their actions (e.g. in the case of a breakdown of communication). We observe that the performance of fictitious play is the same as if all players were able to fully coordinate, when the fraction of the non-coordinating agents, s, is smaller than a critical value s̃. Moreover in both cases, where non-cooperative agents shared and did not share their action with others, the critical value was the same. Above this critical value the performance of fictious play is always affected. Also even in the case where only the 40% of the agents manage to cooperate and share their information the final reward is the 85% of the reference case’s reward, where every agent cooperates.