Spin systems describe particles on a lattice in discrete states at thermal equilibrium. The Ising spin system models magnetic dipoles and captures the continuous phase transition between paramagnetism and ferromagnetism observed in metals.
We consider spin games where players on a lattice control the rate to exchange their states at a Nash equilibrium. The Ising game is an example where the mean field limit can be solved exactly. The solution exhibits a phase transition where the balance between the control cost and the interaction cost tips. We explore how this phase transition appears as a bifurcation in the mean field game system and as a singularity in the solution to the master equation.
Joint work with Mark Cerenzia
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