Are Equivariant Equilibrium Approximators Beneficial?
This work addresses the problem of designing effective equilibrium approximators for game theory applications, providing insights for researchers in AI and multi-agent systems, though it is incremental as it builds on existing equivariant methods.
The paper theoretically analyzes the benefits and limitations of using equivariant architectures for approximating Nash, correlated, and coarse correlated equilibria in normal-form games, showing they offer better generalizability and approximation under permutation-invariant payoff distributions but have drawbacks in equilibrium selection and social welfare.
Recently, remarkable progress has been made by approximating Nash equilibrium (NE), correlated equilibrium (CE), and coarse correlated equilibrium (CCE) through function approximation that trains a neural network to predict equilibria from game representations. Furthermore, equivariant architectures are widely adopted in designing such equilibrium approximators in normal-form games. In this paper, we theoretically characterize benefits and limitations of equivariant equilibrium approximators. For the benefits, we show that they enjoy better generalizability than general ones and can achieve better approximations when the payoff distribution is permutation-invariant. For the limitations, we discuss their drawbacks in terms of equilibrium selection and social welfare. Together, our results help to understand the role of equivariance in equilibrium approximators.