A Link between Sequential Semi-anonymous Nonatomic Games and their Large Finite Counterparts

TL;DR

This paper establishes a connection between equilibria in sequential semi-anonymous nonatomic games and their large finite counterparts, demonstrating how the former can inform near-equilibrium strategies in large finite dynamic games.

Contribution

It introduces a method for using equilibria from SSNGs as near-optimal strategies in large finite games, extending to stationary cases and showing the existence of such equilibria.

Findings

Equilibria in SSNGs can be adopted by players in large finite games for near-equilibrium payoffs.

The equilibria are simple, oblivious to history, and blind to other players' states.

Existence of distributional equilibria in SSNGs is established.

Abstract

We show that equilibria of a sequential semi-anonymous nonatomic game (SSNG) can be adopted by players in corresponding large but finite dynamic games to achieve near-equilibrium payoffs. Such equilibria in the form of random state-to-action rules are parsimonious in form and easy to execute, as they are both oblivious of past history and blind to other players' present states. Our transient results can be extended to a stationary case, where the finite counterparts are special discounted stochastic games. The kind of equilibria we adopt for SSNG are similar to distributional equilibria that are well understood in literature, and they themselves are shown to exist.