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Flow Allocation Games

Author

Listed:
  • Nils Bertschinger

    (Frankfurt Institute of Advanced Studies, Goethe University Frankfurt, 60629 Frankfurt, Germany)

  • Martin Hoefer

    (Institute for Computer Science, Goethe University Frankfurt, 60629 Frankfurt, Germany)

  • Daniel Schmand

    (Center for Industrial Mathematics, University of Bremen, 28359 Bremen, Germany)

Abstract

We study a game-theoretic variant of the maximum circulation problem. In a flow allocation game , we are given a directed flow network. Each node is a rational agent and can strategically allocate any incoming flow to the outgoing edges. Given the strategy choices of all agents, a maximal circulation that adheres to the chosen allocation strategies evolves in the network. Each agent wants to maximize the amount of flow through his or her node. Flow allocation games can be used to express strategic incentives of clearing in financial networks. We provide a cumulative set of results on the existence and computational complexity of pure Nash and strong equilibria as well as tight bounds on the (strong) prices of anarchy and stability. Our results show an interesting dichotomy. Ranking strategies over individual flow units allows us to obtain optimal strong equilibria for many objective functions. In contrast, more intuitive ranking strategies over edges can give rise to unfavorable incentive properties.

Suggested Citation

  • Nils Bertschinger & Martin Hoefer & Daniel Schmand, 2025. "Flow Allocation Games," Mathematics of Operations Research, INFORMS, vol. 50(1), pages 68-89, February.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:1:p:68-89
    DOI: 10.1287/moor.2022.0355
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    References listed on IDEAS

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    2. Trudeau, Christian & Rosenthal, Edward C., 2026. "The pipeline externalities problem," Journal of Mathematical Economics, Elsevier, vol. 122(C).

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