Cooperative Behavior in a Model of Evolutionary Snowdrift Games with $N$-person Interactions

TL;DR

This paper models evolutionary snowdrift games with multi-person interactions, deriving an exact equilibrium equation and showing that cooperation decreases as group size and cost-to-benefit ratio increase, supported by simulations.

Contribution

It introduces an exact $N$-th-order equilibrium equation for multi-person snowdrift games and analyzes how cooperation varies with group size and costs.

Findings

Cooperation decreases with larger group size.

Equilibrium cooperation level scales as 1/N for large N.

Simulation results agree with theoretical predictions.

Abstract

We propose a model of evolutionary snowdrift game with $N$-person interactions and study the effects of multi-person interactions on the emergence of cooperation. An exact $N$-th-order equation for the equilibrium density of cooperators $x^*$ is derived for a well-mixed population using the approach of replicator dynamics. The results show that the extent of cooperation drops with increasing cost-to-benefit ratio and the number $N$ of interaction persons in a group, with $x^{*}\sim1/N$ for large $N$. An algorithm for numerical simulations is constructed for the model. The simulation results are in good agreements with theoretical results of the replicator dynamics.