The Shapley value for shortest path games

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Abstract

In this paper shortest path games are considered. The transportation of a good in a network has costs and benet too. The problem is to divide the prot of the transportation among the players. Fragnelli et al (2000) introduce the class of shortest path games, which coincides with the class of monotone games. They also give a characterization of the Shapley value on this class of games. In this paper we consider further four characterizations of the Shapley value (Shapley (1953)'s, Young (1985)'s, Chun (1989)'s, and van den Brink (2001)'s axiomatizations), and conclude that all the mentioned axiomatizations are valid for shortest path games. Fragnelli et al (2000)'s axioms are based on the graph behind the problem, in this paper we do not consider graph specic axioms, we take TU axioms only, that is, we consider all shortest path problems and we take the view of abstract decision maker who focuses rather on the abstract problem than on the concrete situations.

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• The Shapley value for shortest path games. (deposited 08 Feb 2012 15:51)
  • The Shapley value for shortest path games. (deposited 18 Jun 2012 12:24) [Currently Displayed]