Zero-Determinant Strategies in Iterated Public Goods Game

Pan, Liming; Dong, Hui; Rong, Zhihai; Zhou, Tao

doi:10.1038/srep13096

Cited by 124 publications

(85 citation statements)

References 67 publications

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“…Chen and Zinger analyze the robustness of ZD strategies against evolutionary players and prove that there always exist evolutionary paths for ZD player to obtain the maximum payoff [10]. Press and Dyson's work can be further generalized to multi-player ZD strategies for investigating various social dilemmas, new features and constrains related to participant number and payoff structure have been revealed and the impact of ZD alliance in multi-player games has been studied [11,12]. Furthermore, there are also extensive literatures investigating the significance of ZD strategies in evolutionary game theory and in social networks [8,9,[12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Extortion under uncertainty: Zero-determinant strategies in noisy games

2015

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Repeated game theory has been one of the most prevailing tools for understanding the long-run relationships, which are footstones in building human society. Recent works have revealed a new set of "zero-determinant (ZD)" strategies, which is an important advance in repeated games. A ZD strategy player can exert a unilaterally control on two players' payoffs. In particular he can deterministically set the opponent's payoff, or enforce an unfair linear relationship between the players' payoffs, thereby always seizing an advantageous share of payoffs. One of the limitations of the original ZD strategy, however, is that it does not capture the notion of robustness when the game is subjected to stochastic errors. In this paper, we propose a general model of ZD strategies for noisy repeated games, and find that ZD strategies have high robustness against errors. We further derive the pinning strategy under noise, by which the ZD strategy player coercively set the opponent's expected payoff to his desired level, although his payoff control ability declines with the increase of noise strength. Due to the uncertainty caused by noise, the ZD strategy player cannot secure his payoff to be higher than the opponent's, which implies strong extortions do not exist even under low noise. While we show that the ZD strategy player can still establish a novel kind of extortions, named weak extortions, where any increase of his own payoff always exceeds that of the opponent's by a fixed percentage, and the conditions under which the weak extortions can be realized are more stringent as the noise becomes stronger.

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Section: Introductionmentioning

confidence: 99%

Extortion under uncertainty: Zero-determinant strategies in noisy games

2015

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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%

“…For instance, Press et al [60] proposed the zero-determinant strategy, showing that, in an iterated game, a participant can unilaterally determine the expected payoff of his/her opponents by the pinning strategy, or obtain a higher payoff than his/her opponents by the extortion strategy. Furthermore, Pan et al [63] investigated a multi-player iterated game strategy, which extends the zero-determinant strategy to solve the IPGG problem [66]. …”

Section: Modelmentioning

confidence: 99%

“…To achieve the competitive benefit, the participants may intend to adopt the zero-determinant strategies. Pan et al [63] extended it to the multi-player IPGG problem and demonstrated that, in an infinite repeated game, the long-memory player has no advantages over short-memory players (i.e., the length of memory does not affect the results). Thus, we can assume that the choices of participants in the current round only depend on the outcomes in the last round.…”

Section: Our Approachmentioning

confidence: 99%

“…As described in [63], a long-memory player can be considered as a memory-one player. Then, the game can be characterized by a Markov Chain with a state transition matrix

M

.…”

Section: Our Approachmentioning

confidence: 99%

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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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