Extortion subdues human players but is finally punished in the prisoner’s dilemma

Hilbe, Christian; Röhl, Torsten; Milinski, Manfred

doi:10.1038/ncomms4976

Cited by 97 publications

(137 citation statements)

References 43 publications

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“…According to the analysis above, to get a weak extortion strategy under noise, the following vector equation is required: (13) which can be expanded to:…”

Section: Extortion Under Uncertaintymentioning

confidence: 99%

“…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]. Although initially the evolutionary instability was found for extortion strategies [14], later it is proved that the generous strategies finally dominate in population and are stable in an evolutionary sense [8,15].…”

Section: Introductionmentioning

confidence: 99%

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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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“…According to the analysis above, to get a weak extortion strategy under noise, the following vector equation is required: (13) which can be expanded to:…”

Section: Extortion Under Uncertaintymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extortion under uncertainty: Zero-determinant strategies in noisy games

2015

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“…The mechanisms by which cooperation among humans has evolved and can be sustained have long been of interest to researchers across several disciplines including economics12345678910, sociology11121314, psychology151617, political science181920, evolutionary biology212223242526 and complex systems research27282930. Despite this extraordinary level of attention, numerous questions remain unresolved.…”

mentioning

confidence: 99%

Resilient cooperators stabilize long-run cooperation in the finitely repeated Prisoner’s Dilemma

Mao

Dworkin²,

Suri

et al. 2017

Nat Commun

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Learning in finitely repeated games of cooperation remains poorly understood in part because their dynamics play out over a timescale exceeding that of traditional lab experiments. Here, we report results of a virtual lab experiment in which 94 subjects play up to 400 ten-round games of Prisoner's Dilemma over the course of twenty consecutive weekdays. Consistent with previous work, the typical round of first defection moves earlier for several days; however, this unravelling process stabilizes after roughly one week. Analysing individual strategies, we find that approximately 40% of players behave as resilient cooperators who avoid unravelling even at significant cost to themselves. Finally, using a standard learning model we predict that a sufficiently large minority of resilient cooperators can permanently stabilize unravelling among a majority of rational players. These results shed hopeful light on the long-term dynamics of cooperation, and demonstrate the importance of long-run experiments.

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“…Although competition and natural selection among species drive their evolution and theoretically bring more benefit to defection, the emergence of cooperation behaviors among agents is still ubiquitous in the real world, ranging from biological systems to economic and social systems12345. Therefore, exploring the extensive cooperation behaviors becomes an open challenge and attract the attentions of scientific researchers in a myriad of fields including physics, mathematics, biology and behavioral science678910.…”

mentioning

confidence: 99%

Impact of Social Reward on the Evolution of the Cooperation Behavior in Complex Networks

Chang

Zhang

et al. 2017

Sci Rep

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Social reward, as a significant mechanism explaining the evolution of cooperation, has attracted great attention both theoretically and experimentally. In this paper, we study the evolution of cooperation by proposing a reward model in network population, where a third strategy, reward, as an independent yet particular type of cooperation is introduced in 2-person evolutionary games. Specifically, a new kind of role corresponding to reward strategy, reward agents, is defined, which is aimed at increasing the income of cooperators by applying to them a social reward. Results from numerical simulations show that consideration of social reward greatly promotes the evolution of cooperation, which is confirmed for different network topologies and two evolutionary games. Moreover, we explore the microscopic mechanisms for the promotion of cooperation in the three-strategy model. As expected, the reward agents play a vital role in the formation of cooperative clusters, thus resisting the aggression of defectors. Our research might provide valuable insights into further exploring the nature of cooperation in the real world.

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Extortion subdues human players but is finally punished in the prisoner’s dilemma

Cited by 97 publications

References 43 publications

Extortion under uncertainty: Zero-determinant strategies in noisy games

Extortion under uncertainty: Zero-determinant strategies in noisy games

Resilient cooperators stabilize long-run cooperation in the finitely repeated Prisoner’s Dilemma

Impact of Social Reward on the Evolution of the Cooperation Behavior in Complex Networks

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