On the implementation of zero-determinant strategies in repeated games
arXiv:2306.05597 · doi:10.1016/j.amc.2024.129179
Abstract
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 zero-determinant 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 further deepen our understanding on general mathematical properties of zero-determinant strategies. 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 results assist us to implement zero-determinant strategies in broader situations.
21 pages
References in corpus (11)
- Zero-determinant alliances in multiplayer social dilemmas
- Defection and extortion as unexpected catalysts of unconditional cooperation in structured populations
- Language-based game theory in the age of artificial intelligence
- Extortion under Uncertainty: Zero-Determinant Strategies in Noisy Games
- Zero-determinant strategies in finitely repeated games
- Memory-two zero-determinant strategies in repeated games
- Unbeatable Tit-for-Tat as a Zero-Determinant Strategy
- Necessary and Sufficient Condition for the Existence of Zero-Determinant Strategies in Repeated Games
- Tit-for-Tat Strategy as a Deformed Zero-Determinant Strategy in Repeated Games
- Controlling conditional expectations by zero-determinant strategies
- Unexploitable games and unbeatable strategies