Analysis of Markovian Competitive Situations using Nonatomic Games

TL;DR

This paper demonstrates that equilibria from nonatomic games can be effectively applied to large finite games in dynamic, competitive situations with stochastic elements, providing near-optimal strategies.

Contribution

It extends the application of nonatomic game equilibria to dynamic, stochastic environments with general state spaces, linking stationary equilibria to finite game profiles.

Findings

NG equilibria are applicable to large finite games for near-equilibrium performance.

Random state-to-action maps in NGs are robust to varying levels of player awareness.

A connection between NG stationary equilibrium and large finite game profiles is established.

Abstract

For dynamic situations where the evolution of a player's state is influenced by his own action as well as other players' states and actions, we show that equilibria derived for nonatomic games (NGs) can be used by their large finite counterparts to achieve near-equilibrium performances. We focus on the case with quite general spaces but also with independently generated shocks driving random actions and state transitions. The NG equilibria we consider are random state-to-action maps that pay no attention to players' external environments. They are adoptable by a variety of real situations where awareness of other players' states can be anywhere between full and non-existent. Transient results here also form the basis of a link between an NG's stationary equilibrium (SE) and good stationary profiles for large finite games.