Uniform Value for Recursive Games with Compact Actions

TL;DR

This paper extends the proof of the existence of uniform value to recursive stochastic games with finite states and compact actions, showing both players can have stationary epsilon-optimal strategies.

Contribution

It provides an analogous proof for recursive games, expanding the class of stochastic games where uniform value existence is established.

Findings

Uniform value exists for recursive games with finite states and compact actions.

Both players can have stationary epsilon-optimal strategies.

The proof parallels the approach used for absorbing games.

Abstract

Mertens, Neyman and Rosenberg [MOR, 2009] used the Mertens and Neyman theorem [IJGT, 1981] to prove the existence of uniform value for absorbing games with finite state space and compact action sets. We provide an analogous proof for another class of stochastic games, recursive games with finite state space and compact action sets. Moreover, both players have stationary epsilon-optimal strategies.