Subduing always defecting mutants by multiplayer reactive strategies: Non-reciprocity versus generosity

TL;DR

This paper investigates how multiplayer reactive strategies, incorporating varying levels of generosity and non-reciprocity, can prevent invasion by defectors in repeated prisoner's dilemma games, considering factors like benefit-to-cost ratio and population size.

Contribution

It provides a comparative analysis of generosity versus non-reciprocity in maintaining cooperation against defectors in multiplayer repeated games.

Findings

Generosity can sustain cooperation under certain conditions.

Non-reciprocity offers robustness against defectors in specific scenarios.

Interaction group size influences the effectiveness of strategies.

Abstract

A completely non-generous and reciprocal population of players can create a robust cooperating state that cannot be invaded by always defecting free riders if the interactions among players are repeated for long enough. However, strict non-generosity and strict reciprocity are ideal concepts, and may not even be desirable sometimes. Therefore, to what extent generosity or non-reciprocity can be allowed while still not be swamped by the mutants, is a natural question. In this paper, we not only ask this question but furthermore ask how generosity comparatively fares against non-reciprocity in this context. For mathematical concreteness, we work within the framework of multiplayer repeated prisoner's dilemma game with reactive strategies in a finite and an infinite population; and explore the aforementioned questions through the effects of the benefit to cost ratio, the interaction group size, and the population size.