Complex Strategies in the Iterated Prisoner's Dilemma

A modiied version of the Iterated Prisoner's Dilemma is proposed and examined. At each move of the game a deenitive renunciation to further interactions with the other player is allowed. The results of a simulation are presented. This simulation uses the 95 proposed strategies in a tournament organized by the French edition of Scientiic American. The conclusions are analogous to those of R. Axelrod excepted on the importance of simplicity. Several arguments are given in favor of the view that complexity is necessary to obtain good strategies in the Iterated Prisoner's Dilemma (classical or modiied version), and that there is no limit in the expected strength of strategies: new strategies, more and more complex and eecient, will appear if suuciently rich environments are constructed and simulated. Finally we argue that in such a game, the whole perspective of evolution of intelligence is probable. Thus we have a new argument in favor of a law of \complexiication" in the universe. each player has two choices: cooperate (c) or defect (d). The reward for mutual cooperation c,c] is, say, R=3. The sucker's payoo and the temptation to defect c,d] are S=0 and T=5. The punishment for mutual defection d,d] is P=1. If the game is only played once, then each player gets a higher payoo from defecting than from cooperating, regardless of what the other player does. When the game is played repeatedly we obtain the The exact rules of the game are: 1. The interactions are between pairs of players (i.e., strategies). 2. The number of moves is xed but unknown to the two players (in our experiment, we chose 1000 moves). 3. Each player has two possible choices on each move: cooperate or defect. Choices are made simultaneously. 4. The payoos R, S, T and P have been determined before the game and announced to the players. To see which strategies would be eeective in exploiting the opportunities for cooperation, two round-robin computer tournaments were organized by R. Axelrod 4, 1]. The winner of the two tournaments was the TIT-FOR-TAT, a strategy that uses cooperation on the rst move of the game and then plays whatever the other player chose on the previous move. This performance of the TIT-FOR-TAT strategy did not prove that TIT-FOR-TAT would perform well as an evolutionary strategy. Hence an ecological simulation was conducted. The population dynamics of the ecological simulation was determined by setting the …