Extortion under Uncertainty: Zero-Determinant Strategies in Noisy Games
Dong Hao, Zhihai Rong, Tao Zhou

TL;DR
This paper extends zero-determinant strategies to noisy repeated games, demonstrating their robustness against errors and introducing weak extortion strategies that function under uncertainty.
Contribution
It develops a general model for ZD strategies in noisy environments and introduces the concept of weak extortions, expanding the understanding of strategic control under uncertainty.
Findings
ZD strategies are robust against stochastic errors.
Players can enforce fixed-percentage payoff differences under noise.
Strong extortions are not feasible with noise, but weak extortions are possible.
Abstract
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…
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