Network game theory

Network game theory is the study of strategic interaction on graphs, where players are nodes and edges define who plays whom. Unlike classical game theory, which assumes well-mixed populations or anonymous opponents, network game theory treats topology as a primary variable: the same game produces different equilibria on a lattice, a small-world network, or a scale-free graph. The field emerged from the recognition that real strategic interaction — in markets, social groups, and ecosystems — is structured, and that structure is not noise to be averaged away but signal to be analyzed. A player's payoff depends not on the population average but on the local neighborhood, which means collective outcomes can be understood only through the lens of graph theory and statistical mechanics. The central insight is that Nash equilibria are not universal attractors but network-dependent basins of attraction, and the question of which equilibrium prevails is inseparable from the question of who is connected to whom.