Taxation Can Significantly Enhance The Effectiveness of Reward and Punishment Mechanisms in The N-Person Snowdrift Game

Yihao Liu; Xinsheng Liu

doi:10.62051/nqkdp498

Authors

Yihao Liu
Xinsheng Liu

DOI:

https://doi.org/10.62051/nqkdp498

Keywords:

Cooperation; Evolutionary game theory; NSG; reward; punishment.

Abstract

We extend the reward and punishment mechanisms in the N-person evolutionary snowdrift game (NSG) model by constructing a tax-based pure punishment NSG model and a tax-based pure reward NSG model. Using replicator dynamics, we established two sets of dynamic equations that describe the evolution of the frequencies of the three strategies. Over longer time scales, both systems exhibit stable states involving two strategies, with the exclusion of the third. Introducing tax factors into the reward and punishment mechanisms significantly increases the proportion of cooperators in the steady state and eliminates defectors, with the time to reach the steady state depending on the tax rate. Moreover, we found that tax-based pure reward strategies are more conducive to fostering cooperative behavior within the system compared to tax-based pure punishment strategies. We employed numerical algorithms to simulate the replicator dynamics, and the results of the dynamic equations were in perfect agreement with the numerical simulations.

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