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Stochastic game
About: Stochastic game is a research topic. Over the lifetime, 9493 publications have been published within this topic receiving 202664 citations.
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TL;DR: This paper formulate linear quadratic differential games in which robustness is attained against model uncertainty in infinite-horizon soft-constrained stochastic Nash games involving state-dependent noise in weakly coupled large-scale systems.
58 citations
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TL;DR: In this article, the authors studied a variant of the Dynkin game, where the order by which players are chosen is deterministic, and the probability that the game terminates once the chosen player decides to stop may be strictly less than one.
Abstract: A multi-player Dynkin game is a sequential game in which at every stage one of the players is chosen, and that player can decide whether to continue the game or to stop it, in which case all players receive some terminal payoff. We study a variant of this model, where the order by which players are chosen is deterministic, and the probability that the game terminates once the chosen player decides to stop may be strictly less than one. We prove that a subgame-perfect e-equilibrium in Markovian strategies exists. If the game is not degenerate this e-equilibrium is actually in pure strategies.
58 citations
22 Aug 2004
TL;DR: In this paper, the authors consider infinite antagonistic games over finite graphs and present conditions that, whenever satisfied by the payoff mapping, assure for both players positional (memoryless) optimal strategies.
Abstract: We consider infinite antagonistic games over finite graphs. We present conditions that, whenever satisfied by the payoff mapping, assure for both players positional (memoryless) optimal strategies. To verify the robustness of our conditions we show that all popular payoff mappings, such as mean payoff, discounted, parity as well as several other payoffs satisfy them.
58 citations
TL;DR: In this paper, an alternative definition of regular equilibria is introduced and shown to have the same properties as those definitions already known from the literature, and the system of equations used to define regular equilibrium induces a globally differentiable structure on the space of mixed strategies.
Abstract: An alternative definition of regular equilibria is introduced and shown to have the same properties as those definitions already known from the literature. The system of equations used to define regular equilibria induces a globally differentiable structure on the space of mixed strategies. Interpreting this structure as a vector field, called the Nash field, allows for a reproduction of a number of classical results from a differentiable viewpoint. Moreover, approximations of the Nash field can be used to suitably define indices of connected components of equilibria and to identify equilibrium components which are robust against small payoff perturbations.
58 citations
TL;DR: In this paper, a 2-player random game with supports of size two with high probability has been shown to have a Nash equilibrium with support complexity at least 1 - O(1/log n).
Abstract: We consider Nash equilibria in 2-player random games and analyze a simple Las Vegas algorithm for finding an equilibrium. The algorithm is combinatorial and always finds a Nash equilibrium; on m × n payoff matrices, it runs in time O(m2nloglog n + n2mloglog m) with high probability. Our result follows from showing that a 2-player random game has a Nash equilibrium with supports of size two with high probability, at least 1 - O(1/log n). Our main tool is a polytope formulation of equilibria. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007
58 citations