Dynamic Games with Almost Perfect Information

TL;DR

This paper establishes the existence of subgame-perfect equilibria in dynamic games with almost perfect information, broadening previous results by removing the need for public randomization and continuity conditions.

Contribution

It proves the existence of equilibria in general dynamic games with almost perfect information without requiring public randomization or continuity of state variables.

Findings

Existence of subgame-perfect equilibria in dynamic games with almost perfect information.

Existence of pure-strategy equilibria in perfect-information dynamic games with uncertainty.

Application to a dynamic stochastic oligopoly model.

Abstract

This paper aims to solve two fundamental problems on finite or infinite horizon dynamic games with perfect or almost perfect information. Under some mild conditions, we prove (1) the existence of subgame-perfect equilibria in general dynamic games with almost perfect information, and (2) the existence of pure-strategy subgame-perfect equilibria in perfect-information dynamic games with uncertainty. Our results go beyond previous works on continuous dynamic games in the sense that public randomization and the continuity requirement on the state variables are not needed. As an illustrative application, a dynamic stochastic oligopoly market with intertemporally dependent payoffs is considered.