Equilibria in Repeated Games with Countably Many Players and Tail-Measurable Payoffs

TL;DR

This paper proves that in repeated games with countably many players, finite actions, and tail-measurable payoffs, approximate equilibria always exist, extending equilibrium existence results to more complex game settings.

Contribution

It establishes the existence of epsilon-equilibria in repeated games with infinitely many players and tail-measurable payoffs, a novel extension of equilibrium theory.

Findings

Existence of epsilon-equilibria in complex repeated games

Applicable to games with countably many players

Extends equilibrium results to tail-measurable payoffs

Abstract

We prove that every repeated game with countably many players, finite action sets, and tail-measurable payoffs admits an $\epsilon$-equilibrium, for every $\epsilon > 0$.