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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: In this article, the authors considered play in a two-person zero-sum differential game where the dynamics are given by a differential equation with additive white noise and showed that the minimizing player can achieve the upper value of the game by playing a strategy which is constructed by performing a pointwise min-max on a certain fixed Hamiltonian function.
Abstract: This paper considers play in a two-person zero-sum differential game where the dynamics are given by a differential equation with additive white noise. Feedback strategies are employed. Standard results from control theory show that the maximizing player has an optimal response to any pre-announced strategy of the minimizing player. Here it is shown that the minimizing player can achieve the upper value of the game by playing a strategy which is constructed by performing a pointwise min-max on a certain fixed Hamiltonian function.
50 citations
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TL;DR: In this paper, the authors define and explore the notion of a Dynamic Condorcet Winner (DCW), which extends the concept of a Condorcets winner to dynamic settings and show that, for every DCW, every member of a large class of dynamic majoritarian games has an equivalent equilibrium, and that other equilibria are not similarly portable across this class of games.
Abstract: We define and explore the notion of a Dynamic Condorcet Winner (DCW), which extends the notion of a Condorcet winner to dynamic settings. We show that, for every DCW, every member of a large class of dynamic majoritarian games has an equivalent equilibrium, and that other equilibria are not similarly portable across this class of games. Existence of DCWs is guaranteed when members of the community are sufficiently patient. We characterize sustainable and unsustainable outcomes, study the effects of changes in the discount factor, investigate efficiency properties, and explore the potential for achieving renegotiation-proof outcomes. We apply this solution concept to a standard one-dimensional choice problem wherein agents have single-peaked preferences, as well as to one involving the division of a fixed aggregate payoff.
50 citations
TL;DR: The stochastic stability of a process of learning and evolution in a gift-giving game in which overlapping generations of players are randomly matched to play the game is examined.
50 citations
TL;DR: This article derives a weak version of a dynamic programming principle (DPP) for the corresponding value function and provides an alternative characterization of the value function as a solution of a partial differential equation (PDE) in the sense of discontinuous Viscosity solutions, along with boundary conditions both in Dirichlet and viscosity senses.
49 citations
TL;DR: Two solution concepts of Bayesian optimistic equilibrium strategy and Bayesian maximum chance equilibrium strategy as well as their existence theorems are presented and sufficient and necessary conditions are given for finding the Bayesian equilibrium strategies.
Abstract: In an uncertain bimatrix game, there are two solution concepts of $$(\alpha ,\beta )$$(ź,β)-optimistic equilibrium strategy and $$(u,v)$$(u,v)-maximum chance equilibrium strategy. This paper goes further by assuming that the confidence levels $$\alpha , \beta $$ź,β and payoff levels $$u, v$$u,v are private information. Then, the so-called uncertain bimatrix game with asymmetric information is investigated. Two solution concepts of Bayesian optimistic equilibrium strategy and Bayesian maximum chance equilibrium strategy as well as their existence theorems are presented. Moreover, sufficient and necessary conditions are given for finding the Bayesian equilibrium strategies. Finally, a two-firm advertising problem is analyzed for illustrating our modelling idea.
49 citations