Computable Strategies for Repeated Prisoner′s Dilemma

Knoblauch, Vicki

doi:10.1006/game.1994.1057

Cited by 22 publications

(22 citation statements)

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“…There has already been some research into the complexity of playing repeated and sequential games. For example, determining whether a particular automaton is a best response is N P-complete (BenPorath, 1990); it is N P-complete to compute a best-response automaton when the automata under consideration are bounded (Papadimitriou, 1992); the problem of whether a given player with imperfect recall can guarantee herself a given payoff using pure strategies is N P-complete (Koller and Megiddo, 1992); and in general, best-responding to an arbitrary strategy can even be noncomputable (Knoblauch, 1994;Nachbar and Zame, 1996). In this section, we present a PSPACE-hardness result on the existence of a pure-strategy equilibrium.…”

Section: Pure-strategy Nash Equilibria In Stochastic (Markov) Gamesmentioning

confidence: 99%

New complexity results about Nash equilibria

Conitzer

Sandholm

2008

Games and Economic Behavior

222

270

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We provide a single reduction that demonstrates that in normal-form games: (1) it is N P-complete to determine whether Nash equilibria with certain natural properties exist (these results are similar to those obtained by Gilboa and Zemel [Gilboa, I., Zemel, E., 1989. Nash and correlated equilibria: Some complexity considerations. Games Econ. Behav. 1, 80-93]), (2) more significantly, the problems of maximizing certain properties of a Nash equilibrium are inapproximable (unless P = N P), and (3) it is #P-hard to count the Nash equilibria. We also show that determining whether a pure-strategy Bayes-Nash equilibrium exists in a Bayesian game is N P-complete, and that determining whether a pure-strategy Nash equilibrium exists in a Markov (stochastic) game is PSPACE-hard even if the game is unobserved (and that this remains N P-hard if the game has finite length). All of our hardness results hold even if there are only two players and the game is symmetric.

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Section: Pure-strategy Nash Equilibria In Stochastic (Markov) Gamesmentioning

confidence: 99%

New complexity results about Nash equilibria

Conitzer

Sandholm

2008

Games and Economic Behavior

222

270

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“…The payoff at every game stage is equally weighted (i.e., there is no discounting for future payoffs). Thus, the payoff can be quantified by the liminf-type asymptotic [26]. The authors then proposed a cooperation strategy via randomized inclination to selfish/greedy play (CRISP) to detect and punish selfish nodes.…”

Section: ) Decentralized Access Methodmentioning

confidence: 99%

Applications of Repeated Games in Wireless Networks: A Survey

Hoang

Niyato

et al. 2015

IEEE Commun. Surv. Tutorials

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Abstract-A repeated game is an effective tool to model interactions and conflicts for players aiming to achieve their objectives in a long-term basis. Contrary to static noncooperative games that model an interaction among players in only one period, in repeated games, interactions of players repeat for multiple periods; and thus the players become aware of other players' past behaviors and their future benefits, and will adapt their behavior accordingly. In wireless networks, conflicts among wireless nodes can lead to selfish behaviors, resulting in poor network performances and detrimental individual payoffs. In this paper, we survey the applications of repeated games in different wireless networks. The main goal is to demonstrate the use of repeated games to encourage wireless nodes to cooperate, thereby improving network performances and avoiding network disruption due to selfish behaviors. Furthermore, various problems in wireless networks and variations of repeated game models together with the corresponding solutions are discussed in this survey. Finally, we outline some open issues and future research directions.

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“…Any initial play path determines past stage payoffs through (10) and, jointly with the strategy profile , induces a probability distribution of future stage payoffs. If all stage payoffs are equally weighted (there is no discounting of future payoffs), station 's long-term satisfaction, or utility, can be quantified by the following liminf-type asymptotic [15]: (11) where . Since the are bounded, so are their expectations, hence the limit exists and lower bounds the long-term per stage payoff average.…”

Section: B Greedy Selfish and Honest Configurationsmentioning

confidence: 99%

“…If then with probability (tending to one) phase involves a nonzero number of traversals of the left self-loop. For large , the mean of conditioned on the number of stages between a transition to state H and another phase-up can be expressed as (15) where is the number of traversals of the lower left self-loop, , and is a bounded value. Since , and recalling that , we find that for large the right-hand side of (15) asymptotes to , hence tends to as increases.…”

Section: B Pareto Efficiency and Subgame Perfectionmentioning

confidence: 99%

“…1 (in either case possibly followed by a spell of honest play). Thus, the mean of is given, respectively, by (15) or an expression analogous to (15) with replaced by 0 (the stage payoff in the presence of other stations playing greedy). Consequently, as increases, the probability distribution of concentrates below .…”

Section: B Pareto Efficiency and Subgame Perfectionmentioning

confidence: 99%

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A Game-Theoretic Study of CSMA/CA Under a Backoff Attack

Konorski

2006

IEEE/ACM Trans. Networking

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Abstract-CSMA/CA, the contention mechanism of the IEEE 802.11 DCF medium access protocol, has recently been found vulnerable to selfish backoff attacks consisting in nonstandard configuration of the constituent backoff scheme. Such attacks can greatly increase a selfish station's bandwidth share at the expense of honest stations applying a standard configuration. The paper investigates the distribution of bandwidth among anonymous network stations, some of which are selfish. A station's obtained bandwidth share is regarded as a payoff in a noncooperative CSMA/CA game. Regardless of the IEEE 802.11 parameter setting, the payoff function is found similar to a multiplayer Prisoners' Dilemma; moreover, the number (though not the identities) of selfish stations can be inferred by observation of successful transmission attempts. Further, a repeated CSMA/CA game is defined, where a station can toggle between standard and nonstandard backoff configurations with a view of maximizing a long-term utility. It is argued that a desirable station strategy should yield a fair, Pareto efficient, and subgame perfect Nash equilibrium. One such strategy, called CRISP, is described and evaluated.Index Terms-Ad hoc LAN, game theory, MAC protocol, selfish behavior.

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Computable Strategies for Repeated Prisoner′s Dilemma

Cited by 22 publications

References 0 publications

New complexity results about Nash equilibria

New complexity results about Nash equilibria

Applications of Repeated Games in Wireless Networks: A Survey

A Game-Theoretic Study of CSMA/CA Under a Backoff Attack

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