Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything

TL;DR

This paper investigates the evolutionary stability of Zero Determinant strategies in the Prisoner's Dilemma, revealing they are weakly dominant but not stable, and that recognition-based advantages are short-lived.

Contribution

It demonstrates that ZD strategies are not evolutionarily stable and explores how recognition can temporarily stabilize them against evolving opponents.

Findings

ZD strategies are weakly dominant but not evolutionarily stable.

Recognition-based ZD strategies can be stable but are short-lived.

Opposing strategies evolve to counteract recognition advantages.

Abstract

Zero Determinant (ZD) 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, or else to set the ratio between a ZD player's and their opponent's expected payoff. Here we show that while ZD strategies are weakly dominant, they are not evolutionarily stable and will instead evolve into less coercive strategies. We show that ZD strategies with an informational advantage over other players that allows them to recognize other ZD strategies 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.