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

TL;DR

This study simulates a round-robin tournament of deterministic strategies with complete memory of size three in the iterated prisoner's dilemma, analyzing how payoff matrices and memory influence strategy success.

Contribution

It introduces a comprehensive simulation of strategies with specific memory constraints and examines how different payoff matrices affect tournament outcomes.

Findings

Different strategies win depending on the payoff matrix.

Memory size and payoff details significantly influence strategy success.

Results suggest caution when generalizing iterated prisoner's dilemma outcomes to real systems.

Abstract

In this paper the results of a simulation of a prisoner's dilemma robin-round tournament are presented. In the tournament each participating strategy plays an iterated prisoner's dilemma against each other strategy (round-robin) and as a variant also against itself. The participants of a tournament are all strategies that are deterministic and have the same size of memory with regard to their own and their opponent's past actions: up to three most recent actions of their opponent and up to two most recent actions of their own. A focus is set on the investigation of the influence of the number of iterations, details of the payoff matrix, and the influence of memory size. The main result is that for the tournament as carried out here, different strategies emerge as winners for different payoff matrices, even for different payoff matrices being similar judged on if they fulfill relations T + S = P + R or 2R > 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, one should check if conclusions remain valid, when a different payoff matrix is used.