Recursive Concurrent Stochastic Games

Kousha Etessami, Mihalis Yannakakis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study Recursive Concurrent Stochastic Games (RCSGs), extending our recent analysis of recursive simple stochastic games [14, 15] 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 ε-optimal randomized Stackless & Memoryless (r-SM) strategies, while player 2 (minimizer) has optimal r-SM strategies. Thus, such games are r-SM-determined. These results mirror and generalize in a strong sense the randomized memoryless determinacy results for finite stochastic games, and extend the classic Hoffman-Karp [19] strategy improvement approach from the finite to an infinite state setting. The proofs in our infinite-state setting are very different however.

We show that our upper bounds, even for qualitative termination, can not be improved without a major breakthrough, by giving two reductions: first a P-time reduction from the long-standing square-root sum problem to the quantitative termination decision problem for finite concurrent stochastic games, and then a P-time reduction from the latter problem to the qualitative termination problem for 1-RCSGs.
Original languageEnglish
Title of host publicationICALP (2)
PublisherSpringer-Verlag GmbH
Pages324-335
Number of pages12
Publication statusPublished - 2006

Fingerprint Dive into the research topics of 'Recursive Concurrent Stochastic Games'. Together they form a unique fingerprint.

Cite this