On some variants of prisoner's dilemma dynamics

In this work two variants of Prisoner's dilemma game are given. The first one is related to spite. Spite is the willingness to harm oneself in order to cause more harm to another. An extreme case is when one goes as far as killing himself to harm his enemy. This behavior sometimes occurs in humans. To model it, the standard replicator dynamics is replaced by imitation dynamics. We study the spite replicator dynamics for the prisoner's dilemma game and derive a case where cooperation may arise. The second variant is the prisoner's dilemma loner game. Smale's memory formulation for game is used to study it.