The tragedy of the commons in a multi-population complementarity game

TL;DR

This paper investigates a multi-population complementarity game where populations decide on contributions towards a common goal, revealing that defecting equilibria emerge with more than three populations under certain conditions, based on systematic simulations.

Contribution

It demonstrates how defecting behaviors arise in multi-population complementarity games with simple strategies when the number of populations exceeds three, depending on system parameters.

Findings

Defecting occurs with more than 3 populations under certain conditions.

Multiple equilibria exist, some favoring non-contributing populations.

Simulation results confirm the emergence of defecting strategies.

Abstract

We study a complementarity game with multiple populations whose members' offered contributions are put together towards some common aim. When the sum of the players' offers reaches or exceeds some threshold K, they each receive K minus their own offers. Else, they all receive nothing. Each player tries to offer as little as possible, hoping that the sum of the contributions still reaches K, however. The game is symmetric at the individual level, but has many equilibria that are more or less favorable to the members of certain populations. In particular, it is possible that the members of one or several populations do not contribute anything, a behavior called defecting, while the others still contribute enough to reach the threshold. Which of these equilibria then is attained is decided by the dynamics at the population level that in turn depends on the strategic options the players possess. We find that defecting occurs when more than 3 populations participate in the game, even when the strategy scheme employed is very simple, if certain conditions for the system parameters are satisfied. The results are obtained through systematic simulations.