Abstract
We consider two-player zero-sum stochastic mean payoff games with perfect information. We show that any such game, with a constant number of random positions and polynomially bounded positive transition probabilities, admits a polynomial time approximation scheme, both in the relative and absolute sense.
Highlights
The rise of the Internet has led to an explosion in research in game theory, the mathematical modeling of competing agents in strategic situations
We conclude with a list of open problems (Sect. 3), where we address in particular the question of polynomial smoothed complexity of mean payoff games
As it was noticed already in [21], the BWR model generalizes a variety of games and problems: BWR-games without random positions (VR = ∅) are called cyclic or mean payoff games [16,17,21,33,34]; we call these BW-games
Summary
The rise of the Internet has led to an explosion in research in game theory, the mathematical modeling of competing agents in strategic situations. The central concept in such models is that of a Nash equilibrium, which defines a state where no agent gains an advantage by changing to another strategy. We consider two-player zero-sum stochastic mean payoff games with perfect information. In this case the concept of Nash equilibria coincides with saddle points or mini–max/maxi–min strategies. In an approximate saddle point, no agent can gain a substantial advantage by changing to another strategy. We design approximation schemes for saddle points for such games when the number of random positions is fixed In the conference version of this paper [2], we wrongly claimed that stochastic mean payoff games can be solved in smoothed polynomial time
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