Zero-determinant Strategies for Multi-player Multi-action Iterated Games

He, Xiaofan; Dai, Huaiyu; Ning, Peng; Dutta, Rudra

doi:10.1109/lsp.2016.2517640

Cited by 34 publications

(26 citation statements)

References 6 publications

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“…In Ref. (16), it was shown that every player can have at most one master player, who can play an equalizer strategy on the given player (that is, controlling the expected payoff of the given player), in multi-player multi-action games. Indeed, our general result on the absence of inconsistent ZD strategies (Proposition 1) immediately implies that more than one ZD players cannot simultaneously control the expected payoff of a player to different values.…”

Section: Proposition 1 Any Set Of Zd Strategies Is Consistentmentioning

confidence: 99%

“…The expected payoff vector e = (1,ē T ) T should be given by a non-zero solution of the linear equation α2, · · · , αK). [15] One has SA = (u1, u2, · · · , uK) = 1M b T +SĀ, [16] whereS ≡ (s1, · · · , sN ). The Rouché-Capelli theorem (26) tells us that rankĀ = rank A is a necessary and sufficient condition for the linear equationē TĀ + b T = 0 T K inē to have a solution, that is, for span(Vn) n∈N ′ to be consistent.…”

Section: Appendicesmentioning

confidence: 99%

“…After the pioneering work of Press and Dyson, stability of ZD strategies has been studied in the context of evolutionary game theory (7)(8)(9)(10)(11), and it was found that some kind of ZD strategies, called generous ZD strategies, can stably exist. Although ZD strategy was originally formulated in two-player two-action (iterated prisoner's dilemma) games, ZD strategy was ex-tended to multi-player two-action (iterated social dilemma) games (12,13), two-player multi-action games (14,15), and multi-player multi-action games (16). In addition, ZD strategy was extended to two-player two-action noisy games (17), which is one example of the repeated incomplete-information games.…”

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confidence: 99%

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Linear algebraic structure of zero-determinant strategies in repeated games

Ueda

Tanaka

2020

PLoS ONE

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Zero-determinant (ZD) strategies, a recently found novel class of strategies in repeated games, has attracted much attention in evolutionary game theory. A ZD strategy unilaterally enforces a linear relation between average payoffs of players. Although existence and evolutional stability of ZD strategies have been studied in simple games, their mathematical properties have not been well-known yet. For example, what happens when more than one players employ ZD strategies have not been clarified. In this paper, we provide a general framework for investigating situations where more than one players employ ZD strategies in terms of linear algebra. First, we theoretically prove that a set of linear relations of average payoffs enforced by ZD strategies always has solutions, which implies that incompatible linear relations are impossible. Second, we prove that linear payoff relations are independent of each other under some conditions. These results hold for general incomplete-information games including complete-information games. Furthermore, as an application of linear algebraic formulation, we provide a simple example of a twoplayer game in which one player can simultaneously enforce two linear relations, that is, simultaneously control her and her opponent's average payoffs. All of these results elucidate general mathematical properties of ZD strategies.Repeated games | Zero-determinant strategies | Linear algebra G ame theory is a powerful framework explaining rational behaviors of human beings (1) and evolutionary behaviors of biological systems (2, 3). In a simple example of prisoner's dilemma game, mutual defection is realized as a result of rational thought, even if mutual cooperation is more favorable. On the other hand, when the game is repeated infinite times, cooperation can be realized if players are far-sighted, which is confirmed as folk theorem. Axelrod's famous tournaments on infinitely repeated prisoner's dilemma game (4, 5) also showed that cooperative but retaliating strategy, called the tit-for-tat strategy, is successful in the setting of infinitely repeated game.Recently, in repeated games with complete information, a novel class of strategies, called zero-determinant (ZD) strategy, was discovered (6). Surprisingly, ZD strategy unilaterally enforces a linear relation between average payoffs of all players. A strategy which unilaterally sets her opponent's average payoff (equalizer strategy) is one example. Another example is extortionate strategy in which the player can earn more average payoff than her opponent. ZD strategies contain the well-known tit-for-tat strategy as a special example. After the pioneering work of Press and Dyson, stability of ZD strategies has been studied in the context of evolutionary game theory (7-11), and it was found that some kind of ZD strategies, called generous ZD strategies, can stably exist. Although ZD strategy was originally formulated in two-player two-action (iterated prisoner's dilemma) games, ZD strategy was ex-tended to multi-player two-action (iterate...

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Section: Proposition 1 Any Set Of Zd Strategies Is Consistentmentioning

confidence: 99%

Section: Appendicesmentioning

confidence: 99%

mentioning

confidence: 99%

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Linear algebraic structure of zero-determinant strategies in repeated games

Ueda

Tanaka

2020

PLoS ONE

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“…thereto, , is a nonzero real number. Combining the equations m H = f and (23), we can get the probability that the HEMS will take the active state in different situations as follows: Theorem 2 (see [23,24]). In the repeated game, assuming that the game players ≥ 2, ,min and ,max are, respectively, the maximum and minimum values of row in the × 2 repeated game payoff matrix, where = 1, 2, then…”

Section: Multiperson Zero-determinant Strategy Consider a 3 ×mentioning

confidence: 99%

Research on Defensive Strategy of Real-Time Price Attack Based on Multiperson Zero-Determinant

Xia

Fang

Zou

et al. 2019

Security and Communication Networks

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The smart grid solves the growing load demand of electrical customers through two-way real-time communication of electricity supply and demand sides and home energy management system (HEMS). However, these technical features also bring network security risks to the real-time price signal of the smart grid. The real-time price attack (RTPA) can maliciously raise the real-time price in smart meter, resulting in an increase in electrical customers load demand, causing the extensive damage to the power transmission lines due to overload. In this paper, we based on the behavioral relationship between load demand of electrical customers and real-time price of electricity suppliers (ES), defined the game relationship between RTPA, ES, and electrical customers, established a price elasticity of electricity demand (PEED) model, and proposed a defensive strategy of real-time price attack based on multiperson zero-determinant strategy (MPZDS). The experimental results show that the combination of MPZDS to some extent cut the expected load demand of electrical customers and protect the safety of power transmission lines.

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“…Particularly, in an iterated game, the selfish behavior of participants can lead to a loss for both their opponents and themselves. There are a number of research efforts focused on the iterated game [25,38,60,61,62,63,64,65]. The iterated game problem has been considered to have no unilateral ultimate solution as the results of the game are jointly determined by all participants.…”

Section: Modelmentioning

confidence: 99%

Towards an Iterated Game Model with Multiple Adversaries in Smart-World Systems

Yang

et al. 2018

Sensors

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Diverse and varied cyber-attacks challenge the operation of the smart-world system that is supported by Internet-of-Things (IoT) (smart cities, smart grid, smart transportation, etc.) and must be carefully and thoughtfully addressed before widespread adoption of the smart-world system can be fully realized. Although a number of research efforts have been devoted to defending against these threats, a majority of existing schemes focus on the development of a specific defensive strategy to deal with specific, often singular threats. In this paper, we address the issue of coalitional attacks, which can be launched by multiple adversaries cooperatively against the smart-world system such as smart cities. Particularly, we propose a game-theory based model to capture the interaction among multiple adversaries, and quantify the capacity of the defender based on the extended Iterated Public Goods Game (IPGG) model. In the formalized game model, in each round of the attack, a participant can either cooperate by participating in the coalitional attack, or defect by standing aside. In our work, we consider the generic defensive strategy that has a probability to detect the coalitional attack. When the coalitional attack is detected, all participating adversaries are penalized. The expected payoff of each participant is derived through the equalizer strategy that provides participants with competitive benefits. The multiple adversaries with the collusive strategy are also considered. Via a combination of theoretical analysis and experimentation, our results show that no matter which strategies the adversaries choose (random strategy, win-stay-lose-shift strategy, or even the adaptive equalizer strategy), our formalized game model is capable of enabling the defender to greatly reduce the maximum value of the expected average payoff to the adversaries via provisioning sufficient defensive resources, which is reflected by setting a proper penalty factor against the adversaries. In addition, we extend our game model and analyze the extortion strategy, which can enable one participant to obtain more payoff by extorting his/her opponents. The evaluation results show that the defender can combat this strategy by encouraging competition among the adversaries, and significantly suppress the total payoff of the adversaries via setting the proper penalty factor.

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Zero-determinant Strategies for Multi-player Multi-action Iterated Games

Cited by 34 publications

References 6 publications

Linear algebraic structure of zero-determinant strategies in repeated games

Linear algebraic structure of zero-determinant strategies in repeated games

Research on Defensive Strategy of Real-Time Price Attack Based on Multiperson Zero-Determinant

Towards an Iterated Game Model with Multiple Adversaries in Smart-World Systems

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