Strategy improvement for concurrent reachability and turn based stochastic safety games

K. Chatterjee, L. De Alfaro, T.A. Henzinger, Journal of Computer and System Sciences 79 (2013) 640–657.

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Journal Article | Published | English
Abstract
We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety objective to stay forever in a given set of states, and its dual, the reachability objective to reach a given set of states. First, we present a simple proof of the fact that in concurrent reachability games, for all ε>0, memoryless ε-optimal strategies exist. A memoryless strategy is independent of the history of plays, and an ε-optimal strategy achieves the objective with probability within ε of the value of the game. In contrast to previous proofs of this fact, our proof is more elementary and more combinatorial. Second, we present a strategy-improvement (a.k.a. policy-iteration) algorithm for concurrent games with reachability objectives. Finally, we present a strategy-improvement algorithm for turn-based stochastic games (where each player selects moves in turns) with safety objectives. Our algorithms yield sequences of player-1 strategies which ensure probabilities of winning that converge monotonically (from below) to the value of the game. © 2012 Elsevier Inc.
Publishing Year
Date Published
2013-08-01
Journal Title
Journal of Computer and System Sciences
Acknowledgement
This work was partially supported in part by the NSF grants CCR-0132780, CNS-0720884, CCR-0225610, by the Swiss National Science Foundation, ERC Start Grant Graph Games (Project No. 279307), FWF NFN Grant S11407-N23 (RiSE), and a Microsoft faculty fellows
Volume
79
Issue
5
Page
640 - 657
IST-REx-ID

Cite this

Chatterjee K, De Alfaro L, Henzinger TA. Strategy improvement for concurrent reachability and turn based stochastic safety games. Journal of Computer and System Sciences. 2013;79(5):640-657. doi:10.1016/j.jcss.2012.12.001
Chatterjee, K., De Alfaro, L., & Henzinger, T. A. (2013). Strategy improvement for concurrent reachability and turn based stochastic safety games. Journal of Computer and System Sciences, 79(5), 640–657. https://doi.org/10.1016/j.jcss.2012.12.001
Chatterjee, Krishnendu, Luca De Alfaro, and Thomas A Henzinger. “Strategy Improvement for Concurrent Reachability and Turn Based Stochastic Safety Games.” Journal of Computer and System Sciences 79, no. 5 (2013): 640–57. https://doi.org/10.1016/j.jcss.2012.12.001.
K. Chatterjee, L. De Alfaro, and T. A. Henzinger, “Strategy improvement for concurrent reachability and turn based stochastic safety games,” Journal of Computer and System Sciences, vol. 79, no. 5, pp. 640–657, 2013.
Chatterjee K, De Alfaro L, Henzinger TA. 2013. Strategy improvement for concurrent reachability and turn based stochastic safety games. Journal of Computer and System Sciences. 79(5), 640–657.
Chatterjee, Krishnendu, et al. “Strategy Improvement for Concurrent Reachability and Turn Based Stochastic Safety Games.” Journal of Computer and System Sciences, vol. 79, no. 5, Elsevier, 2013, pp. 640–57, doi:10.1016/j.jcss.2012.12.001.
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