Convergence of Strategies in Simple Co-Adapting Games

Simultaneously co-adapting agents in an uncooperative setting can result in a non-stationary environment where optimisation or learning is difficult and where the agents' strategies may not converge to solutions. This work looks at simple simultaneous-move games with two or three actions and two or three players. Fictitious play is an old but popular algorithm that can converge to solutions, albeit slowly, in self-play in games like these. It models its opponents assuming that they use stationary strategies and plays a best-response strategy to these models. We propose two new variants of fictitious play that remove this assumption and explicitly assume that the opponents use dynamic strategies. The opponent's strategy is predicted using a sequence prediction method in the first variant and a change detection method in the second variant. Empirical results show that our variants converge faster than fictitious play. However, they do not always converge exactly to correct solutions. For change detection, this is a very small number of cases, but for sequence prediction there are many. The convergence of sequence prediction is improved by combining it with fictitious play. Also, unlike in fictitious play, our variants converge to solutions in the difficult Shapley's and Jordan's games.