How the competitive altruism leads to bistable homogeneous states of cooperation or defection

TL;DR

This paper introduces a modified minimal cooperation model incorporating time-dependent altruism based on reputation, revealing two stable states of either widespread cooperation or defection, influenced by competitive altruism.

Contribution

It presents a novel model with dynamic altruism influenced by reputation, demonstrating bistability in cooperation and defection states.

Findings

Two absorbing states of cooperation and defection identified

Reputation-based altruism leads to bistability

Comparison with indirect reciprocity model shows different dynamics

Abstract

Our recent minimal model of cooperation (P. Gawronski et al, Physica A 388 (2009) 3581) is modified as to allow for time-dependent altruism. This evolution is based on reputation of other agents, which in turn depends on history. We show that this modification leads to two absorbing states of the whole system, where the cooperation flourishes in one state and is absent in another one. The effect is compared with the results obtained with the model of indirect reciprocity, where the altruism of agents is constant.