Stable source connection and assignment problems as multi-period shortest path problems

Leanne Streekstra () and Christian Trudeau
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Leanne Streekstra: Budapest University of Technology and Economics

International Journal of Game Theory, 2024, vol. 53, issue 3, No 10, 939-975

Abstract: Abstract We extend the familiar shortest path problem by supposing that agents have demands over multiple periods. This potentially allows agents to combine their paths if their demands are complementary; for instance if one agent only needs a connection to the source in the summer while the other requires it only in the winter. We not only show that the resulting cost sharing problem always generates a totally balanced game, regardless of the number of agents and periods, the cost structure or the demand profile, but that all totally balanced games are representable as multi-period shortest path problems. We then exploit the fact that the model encompasses many well-studied problems to obtain or reobtain balancedness and total balancedness results for source-connection problems, assignment problems and minimum coloring problems.

Keywords: Shortest path; Demand over multiple periods; Cooperative game; Core; Total balancedness; Source-connection; Assignment (search for similar items in EconPapers)
JEL-codes: C71 D63 (search for similar items in EconPapers)
Date: 2024
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Related works:
Working Paper: Stable source connection and assignment problems as multi-period shortest path problems (2022)
Working Paper: Stable source connection and assignment problems as multi-period shortest path problems (2022)
Working Paper: Stable source connection and assignment problems as multi-period shortest path problems (2022)
Working Paper: Stable source connection and assignment problems as multi-period shortest path problems (2020)
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DOI: 10.1007/s00182-024-00896-1

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