Network games with heterogeneous players

Real social and economic networks involve individuals with diverse incentives, yet most studies of network games assume homogeneous preferences or few player types.

We introduce a general framework for binary choice network games with fully heterogeneous payoff structures.

We first show that any such game can be transformed into an equivalent one with conformist, rebel, and stubborn archetypes, preserving equilibria and best response trajectories.

We then establish sufficient conditions for pure strategy Nash equilibrium existence and convergence of best response dynamics on arbitrary networks, while proving that equilibria almost surely vanish in large sparse random networks.

We further develop a deterministic approximation approach that predicts evolutionary trends and equilibrium strategy frequencies from network homophily and heterophily patterns, without computing equilibria explicitly.

Extending the framework to limited information, we prove that dynamics converge either to a unique limited information equilibrium or to a unique stationary distribution, and we derive necessary and sufficient conditions for the existence of the limited information equilibrium.

We validate our predictions using Prisoner's Dilemma games on real social networks that incorporate heterogeneous altruism and peer influence.

These findings together provide a unified framework for equilibrium existence, evolutionary dynamics, and equilibrium outcome prediction in heterogeneous network games.