Scandinavian Working Papers in Economics
Discussion Papers on Economics,
University of Southern Denmark, Department of Economics
No 8/2022: Stable source connection and assignment problems as multi-period shortest path problems
Leanne Streekstra () and Christian Trudeau ()
Additional contact information
Leanne Streekstra: Research Centre of QSMS, Faculty of Economic and Social Sciences, Postal: Research Centre of QSMS, , Faculty of Economic and Social Sciences, Budapest University of Technology and Economics, Budapest, Műegyetem rkp. 3, 1111 Hungary
Christian Trudeau: Department of Economics, University of Windsor, Postal: Department of Economics , University of Windsor, 401 Sunset Avenue, Windsor, Ontario, Canada
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 MSP 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, market problems and minimum coloring problems.
Keywords: shortest path; demand over multiple periods; cooperative game; core; total-balancedness; source-connection; assignment.
Language: English
38 pages, July 15, 2022
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