Wenjie Cao | Searcharxiv

arXiv2026

Equilibria in heterogeneous multi-strategy network games

In this paper, we analyze a multi-strategy network game with three types of players, conformists, rebels, and stubborn agents. Conformists adopt the strategy that is most common among their neighbors, rebels adopt the least common, and stubborn agents adhere to a fixed strategy. We study the existence and structure of pure strategy Nash equilibrium (PNE). On arbitrary networks, we establish sufficient conditions for PNE existence, and prove that in a broad class of large random networks the probability of PNE existence tends to zero as the network size grows. For several specific network architectures, such as complete network, lines, rings, trees, and stars, we derive necessary and sufficient conditions or develop an algorithm for determining PNE existence and characterize the equilibrium strategy frequencies. Collectively, these results offer a unified perspective that PNE is likely to exist when every conformist has more conformist and stubborn neighbors, and fails when the network game has numerous conformist-rebel edges.

econ.TH↗

arXiv2026

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.

econ.TH↗