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Public goods games in directed networks

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  • Papadimitriou, Christos
  • Peng, Binghui

Abstract

Public goods games in undirected networks are generally known to have pure Nash equilibria, which are easy to find. In contrast, we prove that, in directed networks, a broad range of public goods games have intractable equilibrium problems: The existence of pure Nash equilibria is NP-hard to decide, and mixed Nash equilibria are PPAD-hard to find. We define general utility public goods games, and prove a complexity dichotomy result for finding pure equilibria, and a PPAD-completeness proof for mixed Nash equilibria. Even in the divisible goods variant of the problem, where existence is easy to prove, finding the equilibrium is PPAD-complete. Finally, when the treewidth of the directed network is appropriately bounded, we prove that polynomial-time algorithms are possible.

Suggested Citation

  • Papadimitriou, Christos & Peng, Binghui, 2023. "Public goods games in directed networks," Games and Economic Behavior, Elsevier, vol. 139(C), pages 161-179.
    • Handle: RePEc:eee:gamebe:v:139:y:2023:i:c:p:161-179
    DOI: 10.1016/j.geb.2023.02.002
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