Repeated strategies and negative implementation errors shape induced game types in the iterated Prisoner’s Dilemma

Scientific Reports, vol. 16

Abstract

Abstract The iterated Prisoner’s Dilemma is often studied in terms of strategy performance and long-run cooperation. This paper offers an alternative perspective: given a finite set of strategies, the long-run interaction between strategies is interpreted as an induced symmetric 2 × 2 game, and the distribution of such induced game types is examined under implementation errors. Thirteen strategies are used in large-scale computerized round-robin tournaments. For each noise level, long-run per-round payoffs are estimated by repeated sampling with a geometric stopping rule, and each strategy pair is classified into standard symmetric game types using a payoff-ordering taxonomy. The resulting payoff matrices are then used in a discrete-time replicator dynamic to identify which induced game types characterize the evolved population. In addition, a population-weighted transformation is applied in which payoff entries are weighted by encounter frequencies implied by final population shares, yielding a system-level classification of the effective strategic environment. Whereas the encounter-weighted share of induced Prisoner’s Dilemma games is negligible in the final generation under noise-free play, it becomes substantial under negative implementation errors. By contrast, population-weighted classifications concentrate on Concord and Harmony, for the parameter values considered. Bootstrap analysis indicates that the induced game classifications are generally stable under replicate-level resampling.

Authors 1

1. Andreas Duerholt corresponding Aachen Institute of Political Science

   RWTH Aachen University

   Affiliation as printed

   Institute of Political Science, RWTH Aachen University, Theaterstrasse 35-39, 52072, Aachen, Germany