12,070 research outputs found
Markov Decision Processes and Stochastic Games with Total Effective Payoff
We consider finite Markov decision processes (MDPs) with undiscounted total effective payoff. We show that there exist uniformly optimal pure stationary strategies that can be computed by solving a polynomial
number of linear programs. We apply this result to two-player zero-sum stochastic games with perfect information and undiscounted total effective payoff, and derive the existence of a saddle point in uniformly optimal pure stationary strategies
Optimal minimax strategy in a dice game
Each of two players, by turns, rolls a dice several times accumulating the
successive scores until he decides to stop, or he rolls an ace. When stopping,
the accumulated turn score is added to the player account and the dice is given
to his opponent. If he rolls an ace, the dice is given to the opponent without
adding any point. In this paper we formulate this game in the framework of
competitive Markov decision processes (also known as stochastic games), show
that the game has a value, provide an algorithm to compute the optimal minimax
strategy, and present results of this algorithm in three different variants of
the game.Comment: 14 page
Decision Problems for Nash Equilibria in Stochastic Games
We analyse the computational complexity of finding Nash equilibria in
stochastic multiplayer games with -regular objectives. While the
existence of an equilibrium whose payoff falls into a certain interval may be
undecidable, we single out several decidable restrictions of the problem.
First, restricting the search space to stationary, or pure stationary,
equilibria results in problems that are typically contained in PSPACE and NP,
respectively. Second, we show that the existence of an equilibrium with a
binary payoff (i.e. an equilibrium where each player either wins or loses with
probability 1) is decidable. We also establish that the existence of a Nash
equilibrium with a certain binary payoff entails the existence of an
equilibrium with the same payoff in pure, finite-state strategies.Comment: 22 pages, revised versio
Nonzero-sum Stochastic Games
This paper treats of stochastic games. We focus on nonzero-sum games and provide a detailed survey of selected recent results. In Section 1, we consider stochastic Markov games. A correlation of strategies of the players, involving ``public signals'', is described, and a correlated equilibrium theorem proved recently by Nowak and Raghavan for discounted stochastic games with general state space is presented. We also report an extension of this result to a class of undiscounted stochastic games, satisfying some uniform ergodicity condition. Stopping games are related to stochastic Markov games. In Section 2, we describe a version of Dynkin's game related to observation of a Markov process with random assignment mechanism of states to the players. Some recent contributions of the second author in this area are reported. The paper also contains a brief overview of the theory of nonzero-sum stochastic games and stopping games which is very far from being complete.average payoff stochastic games, correlated stationary equilibria, nonzero-sum games, stopping time, stopping games
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