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

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