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 .
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 .
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question-
question:
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behaviour
behavior
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1D
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with nearest neighbor coupling
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the
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a
the
A
or provide strategy
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defection or suppressing cooperation
suppressing cooperation or free riding
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cooperation
providing
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remains ambiguous
is to introduce randomness in strategic choices