Triggers for cooperative behavior in the thermodynamic limit: a case study in Public goods game
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In this work, we aim to answer the question- what triggers cooperative behaviour in the thermodynamic limit by taking recourse to the Public goods game. Using the idea of mapping the Ising model Hamiltonian to payoffs in game theory we calculate the Magnetisation of a 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, while cost can be a trigger for defection or suppressing cooperation. Finally, reward also acts as a trigger for cooperation while the role of inverse temperature (fluctuations in choices) remains ambiguous.
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