The expected prisoner's dilemma - With rationally arising cooperation

Currently, there is no satisfying answer to how cooperation arises rationally in a single-play prisoner's dilemma game with complete information. When player types are known, as well as payoffs and actions, economic analysis through payoff-optimizing computation does not provide a clear path for cooperation. We propose a new form of game-the 'expected' game-and illustrate its implications for theory and practice based on the prisoner's dilemma example. We prove that cooperation can be a rational choice for players in reality in such games defined by a weighted set of payoffs of two or more different reference games.