Zero-determinant strategies under observation errors in repeated games

Mamiya, Azumi; Ichinose, Genki

doi:10.1103/physreve.102.032115

Cited by 19 publications

(7 citation statements)

References 64 publications

(162 reference statements)

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“…With u X := (a AA , a AB , a BA , a BB ) and u Y := (a AA , a BA , a AB , a BB ), the expected payoffs to the two players in the repeated game can then be written explicitly as the following quotients [30,31]:…”

Section: Appendixmentioning

confidence: 99%

Selfish optimization and collective learning in populations

McAvoy,

Mori,

Plotkin

2021

Preprint

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A selfish learner seeks to maximize its own success, disregarding others. When success is measured as payoff in a game played against another learner, mutual selfishness often fails to elicit optimal outcomes. However, learners often operate in populations. Here, we contrast selfish learning among stable pairs of individuals against learning distributed across a population. We consider gradient-based optimization in repeated games like the prisoner's dilemma, which feature multiple Nash equilibria. We find that myopic, selfish learning, when distributed in a population via ephemeral, random encounters, can reverse the dynamics seen in stable pairs and lead to remarkably different outcomes.

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Section: Appendixmentioning

confidence: 99%

Selfish optimization and collective learning in populations

McAvoy,

Mori,

Plotkin

2021

Preprint

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“…Difference between these two effect in the prisoner's dilemma game was detailly investigated in Ref. [20]. Existence of ZD strategies in asynchronous-update social dilemma games was also shown in Ref.…”

Section: Introductionmentioning

confidence: 95%

Necessary and Sufficient Condition for the Existence of Zero-Determinant Strategies in Repeated Games

Ueda¹

2022

J. Phys. Soc. Jpn.

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Zero-determinant strategies are a class of strategies in repeated games which unilaterally control payoffs. Zero-determinant strategies have attracted much attention in studies of social dilemma, particularly in the context of evolution of cooperation. So far, not only general properties of zerodeterminant strategies have been investigated, but zero-determinant strategies have been applied to control in the fields of information and communications technology and analysis of imitation. Here, we provide another example of application of zero-determinant strategies: control of a particle on a lattice. We first prove that zero-determinant strategies, if exist, can be implemented by some one-dimensional transition probability. Next, we prove that, if a two-player game has a non-trivial potential function, a zero-determinant strategy exists in its repeated version. These two results enable us to apply the concept of zero-determinant strategies to control the expected potential energies of two coordinates of a particle on a two-dimensional lattice.

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“…Efforts on various extensions to ZD strategies have been proven fruitful [24][25][26][27], including but not limited to multi-person games [28][29][30][31], noises or errors [32,33], and finitely repeated games [34]. The evolution of ZD strategies has been studied in finite populations [18,35] as well as in structured populations [36].…”

Section: Introductionmentioning

confidence: 99%

The intricate geometry of zero-determinant strategies underlying evolutionary adaptation from extortion to generosity

Chen

Wang

2022

New J. Phys.

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The advent of Zero-Determinant (ZD) strategies has reshaped the study of reciprocity and cooperation in the iterated Prisoner's Dilemma games. The ramification of ZD strategies has been demonstrated through their ability to unilaterally enforce a linear relationship between their own average payoff and that of their co-player. Common practice conveniently represents this relationship by a straight line in the parametric plot of pairwise payoffs. Yet little attention has been paid to studying the actual geometry of the strategy space of all admissible ZD strategies. Here, our work offers intuitive geometric relationships between different classes of ZD strategies as well as nontrivial geometric interpretations of their specific parameterizations. Adaptive dynamics of ZD strategies further reveals the unforeseen connection between general ZD strategies and the so-called equalizers that can set any co-player's payoff to a fixed value. We show that the class of equalizers forming a hyperplane is the critical equilibrium manifold, only part of which is stable. The same hyperplane is also a separatrix of the cooperation-enhancing region where the optimum response is to increase cooperation for each of the four payoff outcomes. Our results shed light on the simple but elegant geometry of ZD strategies that is previously overlooked.

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Zero-determinant strategies under observation errors in repeated games

Cited by 19 publications

References 64 publications

Selfish optimization and collective learning in populations

Selfish optimization and collective learning in populations

Necessary and Sufficient Condition for the Existence of Zero-Determinant Strategies in Repeated Games

The intricate geometry of zero-determinant strategies underlying evolutionary adaptation from extortion to generosity

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