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

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.

arXiv comment25 pages, 6 figures

References in corpus (4)

• Evolutionary potential games on lattices
• Ising model versus normal form game
• Thermodynamics of Evolutionary Games
• Emergence of Cooperation in the thermodynamic limit

Cited by in corpus (8)

• Emergence of Cooperation in the thermodynamic limit
• Thermodynamic susceptibility as a measure of cooperative behavior in social dilemmas
• Quantum Nash equilibrium in the thermodynamic limit
• Nash equilibrium mapping vs Hamiltonian dynamics vs Darwinian evolution for some social dilemma games in the thermodynamic limit
• Spontaneous cooperation for public goods
• Agent-based Modelling of Quantum Prisoner's Dilemma
• Vaccination Dilemma in the thermodynamic limit
• Game susceptibility, Correlation and Payoff capacity as a measure of Cooperative behavior in the thermodynamic limit of some Social dilemmas