research-article

Zero-determinant strategies in repeated asymmetric games

Authors:

Mohammad A. Taha,

Ayman GhoneimAuthors Info & Claims

Volume 369, Issue C

https://doi.org/10.1016/j.amc.2019.124862

Published: 15 March 2020 Publication History

Abstract

Zero-determinant (ZD) strategies are conditional strategies which allow players adopting them to establish a relation between their expected payoffs and those of their opponents. The ZD strategies were investigated in different models including finite and infinite repeated two players’ games, multiplayer games, continuous action spaces and alternating move games. However, all previous studies considered only symmetric games between players, i.e., players have the same strategies and the same associated payoffs, thus the players’ identities are interchangeable without affecting the game's dynamics. In this study, we analytically model and derive the ZD strategies for asymmetric two players’ games, focusing on one-memory strategies and infinite repeated encounters. We derive the analytical bounds of equalizer and extortionate ZD strategies in 2  ×  2 asymmetric games, which differ from the symmetric games case. Furthermore, we derive under what conditions a player using an extortionate ZD strategy will get a higher expected payoff than his/her opponent. Finally using a numerical example, we investigate ZD strategies in 2  ×  2 asymmetric prisoner's dilemma game.

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Cited By

Deng CRong ZWang LWang XDignum FLomuscio AEndriss UNowé A(2021)Modeling Replicator Dynamics in Stochastic Games Using Markov Chain MethodProceedings of the 20th International Conference on Autonomous Agents and MultiAgent Systems10.5555/3463952.3464006(420-428)Online publication date: 3-May-2021
https://dl.acm.org/doi/10.5555/3463952.3464006

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Zero-determinant strategies in repeated asymmetric games

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Published In

cover image Applied Mathematics and Computation

Applied Mathematics and Computation Volume 369, Issue C

Mar 2020

651 pages

ISSN:0096-3003

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Elsevier Inc.

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Elsevier Science Inc.

United States

Publication History

Published: 15 March 2020

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Cited By

Deng CRong ZWang LWang XDignum FLomuscio AEndriss UNowé A(2021)Modeling Replicator Dynamics in Stochastic Games Using Markov Chain MethodProceedings of the 20th International Conference on Autonomous Agents and MultiAgent Systems10.5555/3463952.3464006(420-428)Online publication date: 3-May-2021
https://dl.acm.org/doi/10.5555/3463952.3464006

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