Public Goods Games in Directed Networks with Constraints on Sharing

In a public goods game, every player chooses whether or not to buy a good that all neighboring players will have access to. We consider a setting in which the good is indivisible, neighboring players are out-neighbors in a directed graph, and there is a capacity constraint on their number, k, that can benefit from the good. This means that each player makes a two-pronged decision: decide whether or not to buy and, conditional on buying, choose which k out-neighbors to share access. We examine both pure and mixed Nash equilibria in the model from the perspective of existence, computation, and efficiency. We perform a comprehensive study for these three dimensions with respect to both sharing capacity (k) and the network structure (the underlying directed graph), and establish sharp complexity dichotomies for each.

Authors

• Argyrios Deligkas Royal Holloway, University of London
• Gregory Gutin Royal Holloway University of London, UK Nankai University, China
• Mark Jones Independent Researcher, UK
• Philip R. Neary Royal Holloway University of London, UK
• Anders Yeo University of Southern Denmark, Denmark University of Johannesburg, South Africa

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