博弈收益控制研究进展

In game theory, a single player usually cannot control the payoffs of all players in a game. An exception is the equalizer strategy proposed at the end of the last century for prisoner’s dilemma, with which a player can set their opponent’s payoff to be any designated value in a certain interval, regardless of which strategy the opponent uses. This result was further generalized with the discovery of the zero-determinant (ZD) strategies, which allow a player to unilaterally enforce a linear relationship between his own payoff and that of the opponent. The question of how payoff control can be established has attracted significant attention from computer scientists, control theorists, and evolutionary biologists, and many new results have been subsequently derived. This paper discusses the latest advances in payoff control, enforcing either a linear or nonlinear relation in one-shot or repeated games. In particular, we highlight the above question from four aspects: the concept of payoff control, forms of payoff relation that can be established, strategies that can control payoffs, and the evolutionary behavior of these strategies. We also provide an outlook on the directions for future research.