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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: An example of a zero-sum stochastic game with four states, compact action sets for each player, and continuous payoff and transition functions, such that the discounted value does not converge as the discount factor tends to 0.
Abstract: We give an example of a zero-sum stochastic game with four states, compact action sets for each player, and continuous payoff and transition functions, such that the discounted value does not converge as the discount factor tends to 0, and the value of the n-stage game does not converge as n goes to infinity.

48 citations

Journal ArticleDOI
TL;DR: A particular type of Stackelberg intervention is constructed to show that any positive payoff profile feasible with independent transmission probabilities can be achieved as a Stackellberg equilibrium payoff profile.
Abstract: Interactions among selfish users sharing a common transmission channel can be modeled as a noncooperative game using the game theory framework. When selfish users choose their transmission probabilities independently without any coordination mechanism, Nash equilibria usually result in a network collapse. We propose a methodology that transforms the noncooperative game into a Stackelberg game. Stackelberg equilibria of the Stackelberg game can overcome the deficiency of the Nash equilibria of the original game. A particular type of Stackelberg intervention is constructed to show that any positive payoff profile feasible with independent transmission probabilities can be achieved as a Stackelberg equilibrium payoff profile.We discuss criteria to select an operating point of the network and informational requirements for the Stackelberg game. We relax the requirements and examine the effects of relaxation on performance.

48 citations

Proceedings ArticleDOI
01 Sep 2008
TL;DR: This paper shows how to reformulate two existing distributed spectrum sharing protocols as congestion games, and provides a new formulation by treating frequency-space blocks as resources that is used to construct practical protocols for spectrum sharing between multiple base stations/access points.
Abstract: A fundamental problem in wireless networking is efficient spectrum sharing In this paper we study this problem in the context of decentralized multi-user frequency adaptation, with the objective of designing protocols that are efficient, agile, robust, and incentive-compatible Our approach is based on the theory of congestion games, a class of games that models the competition for resources among multiple selfish players In a congestion game, when a player unilaterally switches her strategy, the change in her own payoff is the same as the change in a global objective known as the potential function Hence any sequence of unilateral improvements results in a pure strategy Nash equilibrium In other words, the game is such that selfish behaviors collectively result in a socially desirable outcome Motivated by the attractive properties of congestion games, this paper sets out to understand how this framework can be used to construct efficient spectrum sharing protocols The key challenge in casting spectrum sharing as a congestion game lies in the proper definition of resources Simply treating wireless channels as resources fails to capture the effect of spatial reuse We first show how to reformulate two existing distributed spectrum sharing protocols as congestion games Such reformulation is done by introducing virtual resources that model pair-wise interference We then provide a new formulation by treating frequency-space blocks as resources We use this formulation to construct practical protocols for spectrum sharing between multiple base stations/access points Different implementation methods based on different signaling assumptions are discussed We further demonstrate that the proposed approach can be readily extended in several aspects, including the modeling of channel bundling and fractional frequency reuse

48 citations

Journal ArticleDOI
01 Jan 2014
TL;DR: Two experiments designed to test cognitive hierarchy, team reasoning, and strong Stackelberg theories against one another in games without obvious, payoff-dominant solutions suggest that each of the theories provides part of the explanation.
Abstract: In common interest games, players generally manage to coordinate their actions on mutually optimal outcomes, but orthodox game theory provides no reason for them to play their individual parts in these seemingly obvious solutions and no justification for choosing the corresponding strategies. A number of theories have been suggested to explain coordination, among the most prominent being versions of cognitive hierarchy theory, theories of team reasoning, and social projection theory (in symmetric games). Each of these theories provides a plausible explanation but is theoretically problematic. An improved theory of strong Stackelberg reasoning avoids these problems and explains coordination among players who care about their co-players’ payoffs and who act as though their co-players can anticipate their choices. Two experiments designed to test cognitive hierarchy, team reasoning, and strong Stackelberg theories against one another in games without obvious, payoff-dominant solutions suggest that each of the theories provides part of the explanation. Cognitive hierarchy Level-1 reasoning, facilitated by a heuristic of avoiding the worst payoff, tended to predominate, especially in more complicated games, but strong Stackelberg reasoning occurred quite frequently in the simpler games and team reasoning in both the simpler and the more complicated games. Most players considered two or more of these reasoning processes before choosing their strategies.

48 citations

Journal ArticleDOI
TL;DR: In this article, the authors consider the undiscounted repeated game obtained by the infinite repetition of such a two-player stage game and show that if supergame strategies are restricted to be computable within Church's thesis, the only pair of payoffs which survives any computable tremble with sufficiently large support is the Pareto-efficient pair.
Abstract: A common interest game is a game in which there exists a unique pair of payoffs which strictly Pareto-dominates all other payoffs. We consider the undiscounted repeated game obtained by the infinite repetition of such a two-player stage game. We show that if supergame strategies are restricted to be computable within Church's thesis, the only pair of payoffs which survives any computable tremble with sufficiently large support is the Pareto-efficient pair. The result is driven by the ability of the players to use the early stages of the game to communicate their intention to play cooperatively in the future.

48 citations


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