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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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Journal ArticleDOI
TL;DR: This paper proposes a Stackelberg game between utility companies and end-users to maximize the revenue of each utility company and the payoff of each user and derive analytical results for the StACkelberg equilibrium of the game and proves that a unique solution exists.
Abstract: Demand Response Management (DRM) is a key component in the smart grid to effectively reduce power generation costs and user bills. However, it has been an open issue to address the DRM problem in a network of multiple utility companies and consumers where every entity is concerned about maximizing its own benefit. In this paper, we propose a Stackelberg game between utility companies and end-users to maximize the revenue of each utility company and the payoff of each user. We derive analytical results for the Stackelberg equilibrium of the game and prove that a unique solution exists. We develop a distributed algorithm which converges to the equilibrium with only local information available for both utility companies and end-users. Though DRM helps to facilitate the reliability of power supply, the smart grid can be succeptible to privacy and security issues because of communication links between the utility companies and the consumers. We study the impact of an attacker who can manipulate the price information from the utility companies. We also propose a scheme based on the concept of shared reserve power to improve the grid reliability and ensure its dependability.

705 citations

Book ChapterDOI
01 Jan 2004
TL;DR: Game theory is a powerful tool for analyzing situations in which the decisions of multiple agents affect each agent's payoff as discussed by the authors and deals with interactive optimization problems, such as games with imperfect information and auctions.
Abstract: Game theory (hereafter GT) is a powerful tool for analyzing situations in which the decisions of multiple agents affect each agent’s payoff. As such, GT deals with interactive optimization problems. While many economists in the past few centuries have worked on what can be considered game-theoretic models, John von Neumann and Oskar Morgenstern are formally credited as the fathers of modern game theory. Their classic book “Theory of Games and Economic Behavior”, von Neumann and Morgenstern (1944), summarizes the basic concepts existing at that time. GT has since enjoyed an explosion of developments, including the concept of equilibrium by Nash (1950), games with imperfect information by Kuhn (1953), cooperative games by Aumann (1959) and Shubik (1962) and auctions by Vickrey (1961), to name just a few. Citing Shubik (2002), “In the 50s ... game theory was looked upon as a curiosum not to be taken seriously by any behavioral scientist. By the late 1980s, game theory in the new industrial organization has taken over ... game theory has proved its success in many disciplines.”

691 citations

Journal ArticleDOI
TL;DR: In this paper, the authors study repeated games in which players observe a public outcome that imperfectly signals the actions played and provide conditions guaranteeing that any feasible, individually rational payoff vector of the stage game can arise as a perfect equilibrium of the repeated game with sufficiently little discounting.
Abstract: The authors study repeated games in which players observe a public outcome that imperfectly signals the actions played. They provide conditions guaranteeing that any feasible, individually rational payoff vector of the stage game can arise as a perfect equilibrium of the repeated game with sufficiently little discounting. The central condition requires that there exist action profiles with the property that, for any two players, no two deviations--one by either player--give rise to the same probability distribution over public outcomes. The results apply to principal-agent, partnership, oligopoly, and mechanism-design models, and to one-shot games with transferable utilities. Copyright 1994 by The Econometric Society.

685 citations

Journal ArticleDOI
TL;DR: Equivalence relations in information and in control functions among different systems are developed and aid in the solving of many general problems by relating their solutions to those of the systems with "perfect memory".
Abstract: General dynamic team decision problems with linear information structures and quadratic payoff functions are studied. The primitive random variables are jointly Gaussian. No constraints on the information structures are imposed except causality. Equivalence relations in information and in control functions among different systems are developed. These equivalence relations aid in the solving of many general problems by relating their solutions to those of the systems with "perfect memory." The latter can be obtained by the method derived in Part I. A condition is found which enables each decision maker to infer the information available to his precedents, while at the same time the controls which will affect the information assessed can be proven optimal. When this condition fails, upper and lower bounds of the payoff function can still be obtained systematically, and suboptimal controls can be obtained.

677 citations

Journal ArticleDOI
TL;DR: In this paper, the authors extend evolutionary game theory to include spatial dimensions, and find that spatial effects can change the outcome of frequency dependent selection and that strategies may coexist that would not coexist in homogeneous populations.
Abstract: Evolutionary game theory can be extended to include spatial dimensions. The individual players are placed in a two-dimensional spatial array. In each round every individual “plays the game” with its immediate neighbours. After this, each site is occupied by its original owner or by one of the neighbours, depending on who scored the highest payoff. These rules specify a deterministic cellular automaton. We find that spatial effects can change the outcome of frequency dependent selection. Strategies may coexist that would not coexist in homogeneous populations. Spatial games have interesting mathematical properties. There are static or chaotically changing patterns. For symmetrical starting conditions we find “dynamical fractals” and “evolutionary kaleidoscopes.” There is a new world to be explored.

673 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023364
2022738
2021462
2020512
2019460
2018483