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We study the complexity of several combinatorial problems in the model ofbinary networked public goods games. In this game, players are represented byvertices in a network, and the action of each player can be either investing ornot investing in a public good. The payoff of each player is determined by thenumber of neighbors who invest and her own action. We study the complexity ofcomputing action profiles that are Nash equilibrium, and those that provide themaximum utilitarian or egalitarian social welfare. We show that these problemsare generally NP-hard but become polynomial-time solvable when the givennetwork is restricted to some special domains, including networks with aconstant bounded treewidth, and those whose critical clique graphs are forests.

A Refined Study of the Complexity of Binary Networked Public Goods Games