Tactical cooperation of defectors in a multi-stage public goods game

TL;DR

This paper investigates how multi-stage public goods games with reinvestment influence cooperation, revealing that the timing and ratio of benefits significantly affect strategic outcomes in structured populations.

Contribution

It introduces a multi-round public goods game model with reinvestment, highlighting the importance of round ratios and the last round in promoting cooperation.

Findings

The last round has a crucial role in achieving full cooperation.

Supporting early rounds can benefit defectors due to accumulated contributions.

The ratio of multiplication factors between rounds influences the dominant strategy.

Abstract

The basic social dilemma is frequently captured by a public goods game where participants decide simultaneously whether to support a common pool or not and after the enhanced contributions are distributed uniformly among all competitors. What if the result of common efforts is {\it not} distributed immediately, but it is reinvested and added to the pool for a next round? This extension may not only result in an enhanced benefit for group members but also opens new strategies for involved players because they may act in distinct rounds differently. In this work we focus on the simplest case when two rounds are considered, but the applied multiplication factors dedicated to a certain round can be different. We show that in structured populations the winning strategy may depend sensitively on the ratio of these factors and the last round has a special importance to reach a fully cooperative state. We also observe that it may pay for defectors to support the first round and after enjoy the extra benefit of accumulated contributions. Full cooperator strategy is only viable if the second round ensures a premium benefit of investments.