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Extortion under uncertainty: Zero-determinant strategies in noisy games
Dong Hao1, Zhihai Rong1, Tao Zhou1,2
1CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, P.R. China.
Summary
Zero-determinant (ZD) strategies in noisy repeated games demonstrate high robustness against errors. While dominant extortions are not possible, contingent extortions can be established under specific conditions.
Area of Science:
- Game Theory
- Mathematical Economics
- Computational Game Theory
Background:
- Repeated game theory is crucial for understanding long-term relationships and societal structures.
- Zero-determinant (ZD) strategies offer players unilateral control over payoffs in repeated games.
- Original ZD strategies lack robustness against stochastic errors in gameplay.
Purpose of the Study:
- To propose a general model for ZD strategies in noisy repeated games.
- To analyze the robustness and limitations of ZD strategies under stochastic errors.
- To investigate new forms of payoff control and extortion in noisy environments.
Main Methods:
- Development of a general model for ZD strategies in noisy repeated games.
- Analysis of strategy robustness against varying levels of stochastic noise.
- Derivation of the 'pinning strategy' under noisy conditions.
Main Results:
- ZD strategies exhibit high robustness against errors in repeated games.
- The pinning strategy allows ZD players to set opponent's expected payoff, but control weakens with noise.
- Dominant extortions are not feasible; contingent extortions are possible but require stricter conditions as noise increases.
Conclusions:
- A novel model of ZD strategies for noisy repeated games is presented.
- ZD strategies offer significant robustness but with limitations on payoff control under noise.
- Contingent extortions represent a new form of payoff manipulation in noisy game theory settings.
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