Tit-for-tat or win-stay, lose-shift?

Abstract

The repeated Prisoner's Dilemma is usually known as a story of tit-for-tat (TFT). This remarkable strategy has won both of Robert Axelrod's tournaments. TFT does whatever the opponent has done in the previous round. It will cooperate if the opponent has cooperated, and it will defect if the opponent has defected. But TFT has two weaknesses: (i) it cannot correct mistakes (erroneous moves) and (ii) a population of TFT players is undermined by random drift when mutant strategies appear which play always-cooperate (ALLC). Another equally simple strategy called ‘win-stay, lose-shift’ (WSLS) has neither of these two disadvantages. WSLS repeats the previous move if the resulting payoff has met its aspiration level and changes otherwise. Here, we use a novel approach of stochastic evolutionary game dynamics in finite populations to study mutation–selection dynamics in the presence of erroneous moves. We compare four strategies: always-defect (ALLD), ALLC, TFT and WSLS. There are two possible outcomes: if the benefit of cooperation is below a critical value then ALLD is selected; if the benefit of cooperation is above this critical value then WSLS is selected. TFT is never selected in this evolutionary process, but lowers the selection threshold for WSLS.