Complex Systems

A Round-Robin Tournament of the Iterated Prisoner's Dilemma with Complete Memory-Size-Three StrategiesDownload PDF

Tobias Kretz
PTV—Planung Transport Verkehr AG
Stumpfstraße 1
D-76131 Karlsruhe, Germany

Abstract

The results of simulating a prisoner's dilemma round-robin tournament are presented. In the tournament, each participating strategy played an iterated prisoner's dilemma against each of the other strategies (round-robin) and as a variant also against itself. The participants of a tournament are all deterministic strategies and have the same memory size regarding their own and their opponent's past actions. Memory sizes of up to three of the most recent actions of their opponent and up to two of their own are discussed. The investigation focused on the influence of the number of iterations, the details of the payoff matrix, and the memory size. The main result for the tournament as carried out here is that different strategies emerge as winners for different payoff matrices. This is true even for different payoff matrices that are judged to be similar if they fulfill relations T + S = P + R or 2 R > T + S. As a consequence of this result, it is suggested that whenever the iterated prisoner's dilemma is used to model a real system that does not explicitly fix the payoff matrix, conclusions should be checked for validity when a different payoff matrix is used.