Resolution of the n-person Prisoners’ Dilemma by Kalai’s Preplay Negotiation Procedure

Abstract

In this paper, we apply the preplay negotiation procedure proposed by Kalai [1981] [Preplay negotiations and the prisoner’s dilemma, Math. Soc. Sci. 1, 375–379] to the [Formula: see text]-person prisoners’ dilemma with [Formula: see text] and examine whether it promotes cooperation. First, we demonstrate that every perfect equilibrium is a proper equilibrium for any extensive-form game in which players have only two alternatives in each information set. We show that if the preplay is carried out once, the preplay game has a proper equilibrium that realizes cooperation. We also show that if the preplay is executed twice, the game has a proper equilibrium that realizes cooperation regardless of the entering action profile (the starting point of the preplays). Finally, we demonstrate that the preplay game consisting of at least two preplays has a proper equilibrium that realizes cooperation.