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The HoneyComb Paradigm for Research on Collective Human Behavior

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Cost Optimisation of Individual-Based Institutional Reward Incentives for Promoting Cooperation in Finite

M H Duong¹, C M Durbac², T A Han³

¹School of Mathematics, University of Birmingham, Birmingham, UK.

Bulletin of Mathematical Biology

|August 5, 2024

Summary

This study optimizes costs for institutional incentives like rewards and punishments to ensure cooperation in finite populations. We found that the cost function for rewarding cooperation is always non-decreasing under specific conditions.

Keywords:

Evolutionary game theory Population dynamics

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Area of Science:

Evolutionary Game Theory
Behavioral Economics
Population Dynamics

Background:

Cooperative behavior is essential for social structures but faces challenges from self-interest.
Institutional incentives (reward, punishment) are proposed to promote cooperation in finite populations.
Understanding the cost-effectiveness of these incentives is crucial for their implementation.

Purpose of the Study:

To optimize the costs of individual-based institutional incentives for maintaining minimal cooperative behavior.
To analyze the impact of reward and punishment schemes on cooperation in finite, well-mixed populations.
To investigate the relationship between incentive design, population size, and cooperative dynamics.

Main Methods:

Analytical study of cost functions for reward incentives under small mutation limits.
Derivation of neutral drift and strong selection limits.
Numerical investigation across various parameter values and mutation rates.

Main Results:

The cost function for the reward incentive is consistently non-decreasing under analytical conditions.
Identified distinct population dynamics in neutral drift (low selection intensity) and strong selection limits.
Numerical simulations confirmed findings for broader parameter ranges.

Conclusions:

Institutional incentives can be designed to ensure minimal cooperation, with cost optimization being a key factor.
The effectiveness and cost of incentives depend on selection intensity and mutation rates.
This research provides a framework for understanding and implementing cost-effective cooperation-promoting strategies.