Aggregate Fictitious Play for Learning in Anonymous Polymatrix Games (Extended Version)
Fictitious play (FP) is a well-studied algorithm that enables agents to learn Nash equilibrium in games with certain reward structures. However, when agents have no prior knowledge of the reward functions, FP faces a major challenge: the joint action space grows exponentially with the number of agents, which slows down reward exploration. Anonymous games offer a structure that mitigates this issue. In these games, the rewards depend only on the actions taken; not on who is taking which action. Under such a structure, we introduce aggregate fictitious play (agg-FP), a variant of FP where each agent tracks the frequency of the number of other agents playing each action, rather than these agents' individual actions. We show that in anonymous polymatrix games, agg-FP converges to a Nash equilibrium under the same conditions as classical FP. In essence, by aggregating the agents' actions, we reduce the action space without losing the convergence guarantees. Using simulations, we provide empirical evidence on how this reduction accelerates convergence.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Computing the Strategy to Commit to in Polymatrix Games (Extended Version)
Leadership games provide a powerful paradigm to model many real-world settings. Most literature focuses on games with a single follower who acts optimistically, breaking ties in favour of the leader. Unfortunately, for r…
Multi-Player Zero-Sum Markov Games with Networked Separable Interactions
We study a new class of Markov games, \emph(multi-player) zero-sum Markov Games} with \emph{Networked separable interactions} (zero-sum NMGs), to model the local interaction structure in non-cooperative multi-agent seque…
Decision MakingSequential Decision MakingGuarantees for Self-Play in Multiplayer Games via Polymatrix Decomposability
Self-play is a technique for machine learning in multi-agent systems where a learning algorithm learns by interacting with copies of itself. Self-play is useful for generating large quantities of data for learning, but h…
Monte Carlo Neural Fictitious Self-Play: Approach to Approximate Nash equilibrium of Imperfect-Information Games
Researchers on artificial intelligence have achieved human-level intelligence in large-scale perfect-information games, but it is still a challenge to achieve (nearly) optimal results (in other words, an approximate Nash…
Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games
While fictitious play is guaranteed to converge to Nash equilibrium in certain game classes, such as two-player zero-sum games, it is not guaranteed to converge in non-zero-sum and multiplayer games. We show that fictiti…
counterfactual