Nonadditive Shortest Paths: Subproblems in Multi-Agent Competitive Network Models

Authors:
Steven A. Gabriel;David Bernstein
Affiliations:
The George Washington University and ICF Consulting, Washington, DC 20052, USA.sgabriel@seas.gwu.edu;James Madison University, Dept. of Computer Science, Harrisonburg, VA, USA. bernstdh@jmu.edu
Venue:
Computational & Mathematical Organization Theory
Year:
2000

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Abstract

A variety of different multi-agent (competitive) networkmodels have been described in the literature. Computationaltechniques for solving such models often involve the iterativesolution of “shortest” path subproblems. Unfortunately, the mosttheoretically interesting models involve nonlinear cost or utilityfunctions and they give rise to nonadditive “shortest” pathsubproblems. This paper both describes some basic existence anduniqueness results for these subproblems and develops a heuristic forsolving them.