Topic
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 work shows that the decision maker considers an alternative for learning or adoption if and only if the expected payoff of the alternative is above a threshold, and describes the optimal learning policy when the outside option is relatively high, and discusses several extensions.
57 citations
TL;DR: In this article, the statistical properties of optimal mixed strategies of large matrix games with random payoff matrices were investigated and analytical expressions for the value of the game and the distribution of strategy strengths were derived.
Abstract: Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties of optimal mixed strategies of large matrix games with random payoff matrices and derive analytical expressions for the value of the game and the distribution of strategy strengths. In particular the fraction of pure strategies not contributing to the optimal mixed strategy of a player is calculated. Both independently distributed as well as correlated elements of the payoff matrix are considered and the results are compared with numerical simulations.
57 citations
TL;DR: This paper explores the coordination between a supplier and a buyer within a decentralized supply chain, through the use of quantity discounts in a game theoretic model, and proposes both cooperative and non-cooperative approaches considering that the product traded experiences a price sensitive demand.
57 citations
TL;DR: In this article, the existence of subgame-perfect equilibria in infinite-action games of perfect information with finitely or countably many players was proved. And they proved that the subgame that is played from date t on depends on the history up to t only as this history affects some vector of state variables.
57 citations
TL;DR: In this paper, the authors derive a new class of continuous-time learning dynamics consisting of a replicator-like drift adjusted by a penalty term that renders the boundary of the game's strategy space repelling, which is equivalent to players keeping an exponentially discounted aggregate of their ongoing payoffs and then using a smooth best response to pick an action based on these performance scores.
Abstract: Starting from a heuristic learning scheme for N-person games, we derive a new class of continuous-time learning dynamics consisting of a replicator-like drift adjusted by a penalty term that renders the boundary of the game's strategy space repelling. These penalty-regulated dynamics are equivalent to players keeping an exponentially discounted aggregate of their ongoing payoffs and then using a smooth best response to pick an action based on these performance scores. Owing to this inherent duality, the proposed dynamics satisfy a variant of the folk theorem of evolutionary game theory and they converge to (arbitrarily precise) approximations of Nash equilibria in potential games. Motivated by applications to traffic engineering, we exploit this duality further to design a discrete-time, payoff-based learning algorithm which retains these convergence properties and only requires players to observe their in-game payoffs: moreover, the algorithm remains robust in the presence of stochastic perturbations and observation errors, and it does not require any synchronization between players.
57 citations