Leveraging Team Correlation for Approximating Equilibrium in Two-Team Zero-Sum Games
CoRR(2024)
摘要
Two-team zero-sum games are one of the most important paradigms in game
theory. In this paper, we focus on finding an unexploitable equilibrium in
large team games. An unexploitable equilibrium is a worst-case policy, where
members in the opponent team cannot increase their team reward by taking any
policy, e.g., cooperatively changing to other joint policies. As an optimal
unexploitable equilibrium in two-team zero-sum games, correlated-team maxmin
equilibrium remains unexploitable even in the worst case where players in the
opponent team can achieve arbitrary cooperation through a joint team policy.
However, finding such an equilibrium in large games is challenging due to the
impracticality of evaluating the exponentially large number of joint policies.
To solve this problem, we first introduce a general solution concept called
restricted correlated-team maxmin equilibrium, which solves the problem of
being impossible to evaluate all joint policy by a sample factor while avoiding
an exploitation problem under the incomplete joint policy evaluation. We then
develop an efficient sequential correlation mechanism, and based on which we
propose an algorithm for approximating the unexploitable equilibrium in large
games. We show that our approach achieves lower exploitability than the
state-of-the-art baseline when encountering opponent teams with different
exploitation ability in large team games including Google Research Football.
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