Finite automata play the repeated prisoner's dilemma

The paper studies two-person supergames. Each player is restricted to carry out his strategies by finite automata. A player's aim is to maximize his average payoff and subject to that, to minimize the number of states of his machine. A solution is defined as a pair of machines in which the choice of machine is optimal for each player at every stage of the game. Several properties of the solution are studied and are applied to the repeated prisoner's dilemma. In particular it is shown that cooperation cannot be the outcome of a solution of the infinitely repeated prisoner's dilemma.