# The value 1 problem under finite-memory strategies for concurrent mean-payoff games

Chatterjee K, Ibsen-Jensen R. 2015. The value 1 problem under finite-memory strategies for concurrent mean-payoff games. Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms vol. 2015, 1018–1029.

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Abstract

We consider concurrent mean-payoff games, a very well-studied class of two-player (player 1 vs player 2) zero-sum games on finite-state graphs where every transition is assigned a reward between 0 and 1, and the payoff function is the long-run average of the rewards. The value is the maximal expected payoff that player 1 can guarantee against all strategies of player 2. We consider the computation of the set of states with value 1 under finite-memory strategies for player 1, and our main results for the problem are as follows: (1) we present a polynomial-time algorithm; (2) we show that whenever there is a finite-memory strategy, there is a stationary strategy that does not need memory at all; and (3) we present an optimal bound (which is double exponential) on the patience of stationary strategies (where patience of a distribution is the inverse of the smallest positive probability and represents a complexity measure of a stationary strategy).

Publishing Year

Date Published

2015-01-01

Proceedings Title

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

Acknowledgement

The research was partly supported by FWF Grant No P 23499-N23, FWF NFN Grant
No S11407-N23 (RiSE), ERC Start grant (279307: Graph Games), and Microsoft faculty fellows award.

Volume

2015

Issue

1

Page

1018-1029

Conference

SODA: Symposium on Discrete Algorithms

Conference Location

San Diego, CA, United States

Conference Date

2015-01-04 – 2015-01-06

ISBN

IST-REx-ID

### Cite this

Chatterjee K, Ibsen-Jensen R. The value 1 problem under finite-memory strategies for concurrent mean-payoff games. In:

*Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms*. Vol 2015. SIAM; 2015:1018-1029. doi:10.1137/1.9781611973730.69Chatterjee, K., & Ibsen-Jensen, R. (2015). The value 1 problem under finite-memory strategies for concurrent mean-payoff games. In

*Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms*(Vol. 2015, pp. 1018–1029). San Diego, CA, United States: SIAM. https://doi.org/10.1137/1.9781611973730.69Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. “The Value 1 Problem under Finite-Memory Strategies for Concurrent Mean-Payoff Games.” In

*Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms*, 2015:1018–29. SIAM, 2015. https://doi.org/10.1137/1.9781611973730.69.K. Chatterjee and R. Ibsen-Jensen, “The value 1 problem under finite-memory strategies for concurrent mean-payoff games,” in

*Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms*, San Diego, CA, United States, 2015, vol. 2015, no. 1, pp. 1018–1029.Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. “The Value 1 Problem under Finite-Memory Strategies for Concurrent Mean-Payoff Games.”

*Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms*, vol. 2015, no. 1, SIAM, 2015, pp. 1018–29, doi:10.1137/1.9781611973730.69.### Export

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arXiv 1409.6690