2014/08/31 by Dong Hao, Zhihai Rong, Tao Zhou · 70 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Decision Sciences · Mathematics · Physics and Astronomy · Social Sciences · #Adversary #Artificial intelligence #Computer science #Economics #Evolutionary Game Theory and Cooperation #Experimental Behavioral Economics Studies #Extortion #Game Theory and Applications #Game theory #Mathematical economics #Mathematics #Noise (video) #Normal-form game #Repeated game #Robustness (evolution) #Set (abstract data type) #Statistics #Stochastic game #Symmetric game #Zero (linguistics) #cs.GT #physics.soc-ph #q-bio.PE
paper · pdf · doi:10.1103/physreve.91.052803
published in Physical Review E 91(5), 052803 (American Physical Society) · 8 pages, 4 figures
openalex publication_date 2015/05/11 · arxiv created 2015/05/13 · arxiv updated 2015/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Repeated game theory has been one of the most prevailing tools for understanding long-running relationships, which are the foundation 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 unilateral 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 sets 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 ensure his payoff to be permanently higher than the opponent's, which implies dominant 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 contingent 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 contingent extortions can be realized are more stringent as the noise becomes stronger.