Necessary and Sufficient Condition for the Existence of Zero-Determinant Strategies in Repeated Games

Abstract

Zero-determinant strategies are a class of memory-one strategies in repeated games which unilaterally enforce linear relationships between payoffs. It has long been unclear for what stage games zero-determinant strategies exist. We provide a necessary and sufficient condition for the existence of zero-determinant strategies. This condition can be interpreted as the existence of two different actions which unilaterally adjust the total value of a linear combination of payoffs. A relation between the class of stage games where zero-determinant strategies exist and other class of stage games is also provided.

12 pages

References in corpus (7)

• Zero-determinant alliances in multiplayer social dilemmas
• Extortion under Uncertainty: Zero-Determinant Strategies in Noisy Games
• Zero-determinant strategies in finitely repeated games
• Memory-two zero-determinant strategies in repeated games
• Tit-for-Tat Strategy as a Deformed Zero-Determinant Strategy in Repeated Games
• Conditions for the existence of zero-determinant strategies under observation errors in repeated games
• Unbeatable Tit-for-Tat as a Zero-Determinant Strategy

Cited by in corpus (6)

• On the implementation of zero-determinant strategies in repeated games
• Autocratic strategies in Cournot oligopoly game
• Unexploitable games and unbeatable strategies
• Properties of zero-determinant strategies in multichannel games
• Zero-determinant strategies in repeated continuously-relaxed games
• On the existence of fair zero-determinant strategies in the periodic prisoner's dilemma game