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• W2245890606 abstract "We suggest a new algorithm for two-person zero-sum undiscounted stochastic games focusing on stationary strategies. Given a positive real $$varepsilon $$ , let us call a stochastic game $$varepsilon $$ -ergodic, if its values from any two initial positions differ by at most $$varepsilon $$ . The proposed new algorithm outputs for every $$varepsilon >0$$ in finite time either a pair of stationary strategies for the two players guaranteeing that the values from any initial positions are within an $$varepsilon $$ -range, or identifies two initial positions u and v and corresponding stationary strategies for the players proving that the game values starting from u and v are at least $$varepsilon /24$$ apart. In particular, the above result shows that if a stochastic game is $$varepsilon $$ -ergodic, then there are stationary strategies for the players proving $$24varepsilon $$ -ergodicity. This result strengthens and provides a constructive version of an existential result by Vrieze (Stochastic games with finite state and action spaces. PhD thesis, Centrum voor Wiskunde en Informatica, Amsterdam, 1980) claiming that if a stochastic game is 0-ergodic, then there are $$varepsilon $$ -optimal stationary strategies for every $$varepsilon > 0$$ . The suggested algorithm is based on a potential transformation technique that changes the range of local values at all positions without changing the normal form of the game." @default.
• W2245890606 created "2016-06-24" @default.
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• W2245890606 date "2016-07-08" @default.
• W2245890606 modified "2023-09-25" @default.
• W2245890606 title "A Potential Reduction Algorithm for Two-Person Zero-Sum Mean Payoff Stochastic Games" @default.
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• W2245890606 doi "https://doi.org/10.1007/s13235-016-0199-x" @default.
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