Trembles may support cooperation in a repeated prisoner's dilemma game

This paper studies the effect of ‘trembles’ in a repeated prisoner's dilemma game. Previous studies have focused on the detrimental effects of trembles and sought to find error-proof strategies. This paper examines a potential benefit of mistakes in play. Even though mistakes reduce the effectiveness of punishment, it will be shown that in the presence of trembles, some conditional cooperative strategies become asymptotically stable. The paper also shows that the effect of trembles depends in a surprising way on the benefit-cost ratio in the model: benefits must be neither too low nor too high if stability of conditional cooperation is to arise.