Cost optimisation of hybrid institutional incentives for promoting cooperation in finite populations

TL;DR

This paper analyzes how hybrid incentives combining rewards and punishments can be optimally designed to promote cooperation cost-effectively in finite populations, with theoretical and numerical insights.

Contribution

It introduces a rigorous framework for optimizing mixed institutional incentives, revealing phase transitions and providing algorithms for cost-effective cooperation promotion.

Findings

Hybrid incentives are more cost-efficient than pure incentives.

Identified critical thresholds for incentive strength affecting cost and cooperation.

Provided algorithms for optimal incentive cost determination.

Abstract

In this paper, we rigorously study the problem of cost optimisation of hybrid (mixed) institutional incentives, which are a plan of actions involving the use of reward and punishment by an external decision-maker, for maximising the level (or guaranteeing at least a certain level) of cooperative behaviour in a well-mixed, finite population of self-regarding individuals who interact via cooperation dilemmas (Donation Game or Public Goods Game). We show that a mixed incentive scheme can offer a more cost-efficient approach for providing incentives while ensuring the same level or standard of cooperation in the long-run. We establish the asymptotic behaviour (namely neutral drift, strong selection, and infinite-population limits). We prove the existence of a phase transition, obtaining the critical threshold of the strength of selection at which the monotonicity of the cost function changes and providing an algorithm for finding the optimal value of the individual incentive cost. Our analytical results are illustrated with numerical investigations. Overall, our analysis provides novel theoretical insights into the design of cost-efficient institutional incentive mechanisms for promoting the evolution of cooperation in stochastic systems.