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In the Binary Networked Public Goods game, every player needs to decide ifshe participates in a public project whose utility is shared equally by thecommunity. We study the problem of deciding if there exists a pure strategyNash equilibrium (PSNE) in such games. The problem is already known to beNP-complete. We provide fine-grained analysis of this problem under the lens ofparameterized complexity theory. We consider various natural graph parametersand show either W[1]-hardness or exhibit an FPT algorithm. We finally exhibitsome special graph classes, for example path, cycle, bi-clique, complete graph,etc., which always have a PSNE if the utility function of the players are fullyhomogeneous.

On Parameterized Complexity of Binary Networked Public Goods Game