Evolutionary instability of zero-determinant strategies demonstrates that winning is not everything

TLDR

Zero‑determinant strategies are probabilistic, conditional tactics that can unilaterally fix an opponent’s expected payoff or the payoff ratio in iterated Prisoner’s Dilemma games, regardless of the opponent’s strategy. The study finds that zero‑determinant strategies are not evolutionarily stable and tend to evolve toward less coercive behavior, although an informational advantage can temporarily stabilize them before counter‑strategies emerge.

Abstract

Zero-determinant strategies are a new class of probabilistic and conditional strategies that are able to unilaterally set the expected payoff of an opponent in iterated plays of the Prisoner’s Dilemma irrespective of the opponent’s strategy (coercive strategies), or else to set the ratio between the player’s and their opponent’s expected payoff (extortionate strategies). Here we show that zero-determinant strategies are at most weakly dominant, are not evolutionarily stable, and will instead evolve into less coercive strategies. We show that zero-determinant strategies with an informational advantage over other players that allows them to recognize each other can be evolutionarily stable (and able to exploit other players). However, such an advantage is bound to be short-lived as opposing strategies evolve to counteract the recognition. In iterated Prisoner’s Dilemma games, zero-determinant strategies are able to define the opponent’s payoff regardless of the opponent’s strategy. Here the authors show that zero-determinant strategies are not evolutionary stable in adapting populations, and instead evolve into non-coercive strategies.