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

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.