Cooperative Solutions for Network Games with Quadratic Utilities

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This paper analyzes the public goods model with linear quadratic utilities in which each player determines the intensity of the activity they take, which can also be described as a network game with local payoff complementarity, as well as positive payoffs and negative quadratic costs. Players play cooperative games with each other, and cooperative solutions when the game is the planner’s optimal concern for the collective, describing each player’s optimal action in maximizing the individual and public interest. They are implemented programmatically to facilitate simple computations. In these games, players’ activities can be linked to their positions in the local interaction network. The cooperative actions taken by any player are proportional to their Katz-Bonacich centrality in a complementary linear quadratic game. In other words, higher Katz-Bonacich centrality, higher action. We then use a comparative statics framework to analyse the effect that changes in individual variables have on cooperative actions.