Friendly-rivalry solution to the iterated $n$-person public-goods game

TL;DR

This paper develops a friendly-rivalry strategy for the iterated n-person public-goods game that promotes cooperation and is robust against mutants, demonstrated through theoretical construction and evolutionary simulations.

Contribution

It generalizes the friendly-rivalry strategy from the Prisoner's Dilemma to the n-person public-goods game, introducing a decision rule based on the previous 2n-1 rounds.

Findings

The strategy ensures cooperation and robustness for n=2.

Simulation results show high performance across various conditions.

The strategy maintains evolutionary stability against mutant strategies.

Abstract

Repeated interaction promotes cooperation among rational individuals under the shadow of future, but it is hard to maintain cooperation when a large number of error-prone individuals are involved. One way to construct a cooperative Nash equilibrium is to find a `friendly-rivalry' strategy, which aims at full cooperation but never allows the co-players to be better off. Recently it has been shown that for the iterated Prisoner's Dilemma in the presence of error, a friendly rival can be designed with the following five rules: Cooperate if everyone did, accept punishment for your own mistake, punish defection, recover cooperation if you find a chance, and defect in all the other circumstances. In this work, we construct such a friendly-rivalry strategy for the iterated $n$-person public-goods game by generalizing those five rules. The resulting strategy makes a decision with referring to the previous $m=2n-1$ rounds. A friendly-rivalry strategy for $n=2$ inherently has evolutionary robustness in the sense that no mutant strategy has higher fixation probability in this population than that of a neutral mutant. Our evolutionary simulation indeed shows excellent performance of the proposed strategy in a broad range of environmental conditions when $n= 2$ and $3$.