Optimal Control of Fractional Punishment in Optional Public Goods Game

TL;DR

This paper formulates an optimal control approach using fractional punishment to enhance cooperation in Public Goods Games, providing insights into effective penalization strategies that outperform constant punishment methods.

Contribution

It introduces a novel optimal control framework with fractional punishment for PGG, offering a new method to improve cooperation efficiently.

Findings

Optimal controller outperforms constant fractional punishment

Provides insights into period and size of penalization

Enhances cooperation with less cost

Abstract

Punishment is probably the most frequently used mechanism to increase cooperation in Public Goods Games (PGG); however, it is expensive. To address this problem, this paper introduces an optimal control problem that uses fractional punishment to promote cooperation. We present a series of computational experiments illustrating the effects of single and combined terms of the optimization cost function. In the findings, the optimal controller outperforms the use of constant fractional punishment and gives an insight into the period and size of the penalization to be implemented with respect to the defection in the game.