Pure strategy equilibrium in finite weakly unilaterally competitive games

Iimura, Takuya; Watanabe, Takahiro

doi:10.1007/s00182-015-0481-y

Cited by 11 publications

(7 citation statements)

References 10 publications

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“…For the attacker, whether his/her type is H, M, or L, he/she can take one of the I, A, or D actions. If we denote (X, Y, Z) the strategy that type-H attacker plays X, type-M attacker plays Y while type-L attacker plays Z, then there would be 3 3 = 27 pure strategies [26] for σ. For the ICPS defender, we let (X, Y, Z) represent the strategy for the ICPS defender to play X, Y , and Z under the information sets H, F, and N, respectively.…”

Section: Equilibria Analysismentioning

confidence: 99%

Anti-Honeypot Enabled Optimal Attack Strategy for Industrial Cyber-Physical Systems

Xiao

Shi

et al. 2020

IEEE Open J. Comput. Soc.

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Honeypots have been widely used in the security community to understand the cyber threat landscape, for example to study unauthorized penetration attempts targeting industrial cyber-physical systems (ICPS) and observing the behaviors in such activities. However, some better-resourced cyber attackers may attempt to identify honeypots and develop strategies to compromise them, aka anti-honeypot. In this paper, we present an anti-honeypot enabled optimal attack strategy for ICPS, by employing a novel game-theoretical approach. Specifically, the interactions between the attacker and ICPS defender are captured with a proposed hybrid signaling and repeated game, i.e., a non-cooperative two-player one-shot game with incomplete information. By taking into account both various possible defenses of an ICPS and diverse offensive acts of attackers, a Nash equilibrium is derived, which exhibits an optimal attack strategy for attackers with varying technical sophistication. Extensive simulation experiments on multiple test cases demonstrate that, the derived strategy offers the attackers an optimal tactic to compromise the target ICPS protected by honeypots, while having only incomplete knowledge of the defensive mechanisms.

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Section: Equilibria Analysismentioning

confidence: 99%

Anti-Honeypot Enabled Optimal Attack Strategy for Industrial Cyber-Physical Systems

Xiao

Shi

et al. 2020

IEEE Open J. Comput. Soc.

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“…The wuc games strictly include the classes of zero-sum and strictly competitive games. Recently, interest in wuc games was reignited in view of the sufficient conditions for the existence of pure strategy equilibria in such games that were given by Iimura and Watanabe [2016].…”

Section: Commitment Value and Nash Equilibria Payoffs In Generalizati...mentioning

confidence: 99%

On the Commitment Value and Commitment Optimal Strategies in Bimatrix Games

Leonardos

Melolidakis

2018

Int. Game Theory Rev.

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Given a bimatrix game, the associated leadership or commitment games are defined as the games at which one player, the leader, commits to a (possibly mixed) strategy and the other player, the follower, chooses his strategy after having observed the irrevocable commitment of the leader. Based on a result by von Stengel and Zamir [2010], the notions of commitment value and commitment optimal strategies for each player are discussed as a possible solution concept. It is shown that in non-degenerate bimatrix games (a) pure commitment optimal strategies together with the follower's best response constitute Nash equilibria, and (b) strategies that participate in a completely mixed Nash equilibrium are strictly worse than commitment optimal strategies, provided they are not matrix game optimal. For various classes of bimatrix games that generalize zero sum games, the relationship between the maximin value of the leader's payoff matrix, the Nash equilibrium payoff and the commitment optimal value is discussed. For the Traveler's Dilemma, the commitment optimal strategy and commitment value for the leader are evaluated and seem more acceptable as a solution than the unique Nash equilibrium. Finally, the relationship between commitment optimal strategies and Nash equilibria in 2 × 2 bimatrix games is thoroughly examined and in addition, necessary and sufficient conditions for the follower to be worse off at the equilibrium of the leadership game than at any Nash equilibrium of the simultaneous move game are provided.

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“…In fact, although the Nash theorem is one of the most important results in game theory, it only guarantees that an equilibrium (pure or mixed) exists and therefore a part of the problem of existence of equilibrium points in pure strategies remains unsolved. While most of the subsequent research on the problem of existence of equilibrium points in games have generalized Nash's theorem in more general and abstract in nite spaces, (for example, see [5][6][7][8][9][10][11][12][13][14][15][16][17][19][20][21][22][23][24][25][26]), fewer studies have retained the nite strategy space assumption (3 for example, see [27][28][29][30][31][32]). (It is important to note that the generalization of the problem to in nite spaces with a richer topological structure does not solve the pure strategy equilibrium problem when the space is nite and mixed strategies are not allowed).…”

Section: Introductionmentioning

confidence: 99%

“…More recently, the authors of [30] gave a related sufficient condition for the existence of pure strategy Nash equilibria for the class of finite games (with n > 2 players) that satisfy some unilaterally competitive (UC) property which was first developed by the authors of [35]. (4 While the authors of [35] gave some interesting properties of the UC class of games, the authors of [28] show in the first place that all quasi-concave, symmetric UC games have a symmetric pure strategy equilibrium and more recently (in [30]) that all UC games with at least three players have a Nash equilibrium). Another class of games that have the pure strategy Nash equilibrium property was given by the authors of [36,37] who proved the existence of equilibrium for all symmetric quasi-concave finite games two-player zero-sum games.…”

Section: Introductionmentioning

confidence: 99%

On a Fixed Point Theorem for General Multivalued Mappings on Finite Sets with Applications in Game Theory

Luckraz

2022

Journal of Mathematics

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We propose a new fixed point theorem that completely characterizes the existence of fixed points for multivalued maps on finite sets. Our result can be seen as a generalization of Abian’s fixed point theorem. In the context of finite games, our result can be used to characterize the existence of a Nash equilibrium in pure strategies and can therefore distinguish pure strategy equilibria from mixed strategy equilibria in the celebrated Nash theorem.

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Pure strategy equilibrium in finite weakly unilaterally competitive games

Cited by 11 publications

References 10 publications

Anti-Honeypot Enabled Optimal Attack Strategy for Industrial Cyber-Physical Systems

Anti-Honeypot Enabled Optimal Attack Strategy for Industrial Cyber-Physical Systems

On the Commitment Value and Commitment Optimal Strategies in Bimatrix Games

On a Fixed Point Theorem for General Multivalued Mappings on Finite Sets with Applications in Game Theory

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