Evolutionary stability in the n-person iterated prisoner's dilemma

The iterated prisoner's dilemma game has been used extensively in the study of the evolution of cooperative behaviours in social and biological systems. The concept of evolutionary stability provides a useful tool to analyse strategies for playing the game. Most results on evolutionary stability, however, are based on the 2-person iterated prisoner's dilemma game. This paper extends the results in the 2-person game and shows that no finite mixture of pure strategies in the n-person iterated prisoner's dilemma game can be evolutionarily stable, where n > 2. The paper also shows that evolutionary stability can be achieved if mistakes are allowed in the n-person game.