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We analyze, on a random graph, a diffusive strategic dynamics with pairwiseinteractions, where nor Glauber prescription, neither detailed balance hold. Weobserve numerically that such a dynamics reaches a well defined steady statethat fulfills a shift property: the critical temperature of the canonicalferromagnetic phase transition is higher with respect to the expectedequilibrium one, known both numerically via Glauber relaxation or Monte Carlosimulations as well as analytically via cavity techniques or replicaapproaches. We show how the relaxed states of this kind of dynamics can bedescribed by statistical mechanics equilibria of a diluted p-spin model, for asuitable non-integer real p. Several implications from both theoretical physicsand quantitative sociology points of view are discussed.

Effective Interactions in Group Competition with Strategic Diffusive Dynamics