Triggers for cooperative behavior in the thermodynamic limit: a case study in Public goods game

TL;DR

This paper investigates how punishment, reward, and cost influence cooperative behavior in the Public Goods game by modeling it with an Ising model analogy, revealing phase transitions and the role of external factors in the thermodynamic limit.

Contribution

It introduces a novel mapping of the Public Goods game to an Ising model to analyze phase transitions and the effects of external triggers on cooperation in large populations.

Findings

Punishment acts as an external field promoting cooperation.

Cost suppresses cooperative behavior and encourages free riding.

Reward also triggers cooperation, with fluctuations adding randomness.

Abstract

In this work, we aim to answer the question: what triggers cooperative behavior in the thermodynamic limit by taking recourse to the Public goods game. Using the idea of mapping the 1D Ising model Hamiltonian with nearest neighbor coupling to payoffs in the game theory we calculate the Magnetisation of the game in the thermodynamic limit. We see a phase transition in the thermodynamic limit of the two player Public goods game. We observe that punishment acts as an external field for the two player Public goods game triggering cooperation or provide strategy, while cost can be a trigger for suppressing cooperation or free riding. Finally, reward also acts as a trigger for providing while the role of inverse temperature (fluctuations in choices) is to introduce randomness in strategic choices.