Forgiveness is an Adaptation in Iterated Prisoner's Dilemma with Memory

TL;DR

The paper investigates memory-limited IPD by extending forgetting strategies and evaluating them in homogeneous and heterogeneous populations. By modeling memory as capacity $M$ with memory ratio $bc = M / N$ and using a perceived cooperation metric $t_{ij}$, the authors compare six forgetting strategies. In heterogeneous environments, forgetting defectors yields the strongest performance, suggesting that forgiving defectors is an adaptive response in diverse populations, whereas homogeneous environments favor different strategies. The work advances understanding of cooperation under memory constraints and provides a framework and code for replicating the IPD-with-memory experiments.

Abstract

The Prisoner's Dilemma is used to represent many real life phenomena whether from the civilized world of humans or from the wild life of the other living. Researchers working on iterated prisoner's dilemma (IPD) with limited memory inspected the outcome of different forgetting strategies in homogeneous environment, within which all agents adopt the same forgetting strategy at a time. In this work, with the intention to represent real life more realistically, we improve existing forgetting strategies, offer new ones, and conduct experiments in heterogeneous environment that contains mixed agents and compare the results with previous research as well as homogeneous environment. Our findings show that the outcome depends on the type of the environment, and is just the opposite for homogeneous and heterogeneous ones, opposing the existing literature in IPD. Consequently, forgetting and forgiving defectors is the supreme memory management strategy in a competitive, heterogeneous environment. Therefore, forgiveness is an adaptation.

Figures (2)

• Figure 1: Payoff ratio $\phi$ of cooperators, that is, agents with $\rho > 0.5$ in homogeneous and heterogeneous environments.
• Figure 2: Individuals payoffs in heterogeneous environment