Flow Allocation Games

Nils Bertschinger (), Martin Hoefer () and Daniel Schmand ()
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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

Mathematics of Operations Research, 2025, vol. 50, issue 1, 68-89

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.

Keywords: 68Q25; 68W40; 91A43; 91G45; equilibrium computation; flow game; maximum circulation problem; financial networks (search for similar items in EconPapers)
Date: 2025
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