Recursive Concurrent Stochastic Games
Kousha Etessami, Mihalis Yannakakis

TL;DR
This paper analyzes recursive concurrent stochastic games, characterizing their values, establishing PSPACE decidability for termination, and demonstrating strategy optimality and determinacy in an infinite-state setting.
Contribution
It extends analysis of recursive stochastic games to concurrent settings, providing new decidability results, strategy improvement techniques, and determinacy proofs for single-exit recursive concurrent stochastic games.
Findings
Characterized the value of 1-RCSG termination as a least fixed point of nonlinear minimax equations.
Proved PSPACE decidability for the quantitative termination problem.
Established that player 1 has -optimal randomized strategies, and player 2 has optimal strategies, showing r-SM-determinacy.
Abstract
We study Recursive Concurrent Stochastic Games (RCSGs), extending our recent analysis of recursive simple stochastic games to a concurrent setting where the two players choose moves simultaneously and independently at each state. For multi-exit games, our earlier work already showed undecidability for basic questions like termination, thus we focus on the important case of single-exit RCSGs (1-RCSGs). We first characterize the value of a 1-RCSG termination game as the least fixed point solution of a system of nonlinear minimax functional equations, and use it to show PSPACE decidability for the quantitative termination problem. We then give a strategy improvement technique, which we use to show that player 1 (maximizer) has \epsilon-optimal randomized Stackless & Memoryless (r-SM) strategies for all \epsilon > 0, while player 2 (minimizer) has optimal r-SM strategies. Thus, such games…
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