The Shapley value for shortest path games

Pintér, Miklós and Radványi, Anna (2013) The Shapley value for shortest path games. CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH, 21 (4). pp. 769-781. ISSN 1435-246X

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Abstract

The shortest path games are considered in this paper. The transportation of a good in a network has costs and benefits. The problem is to divide the profit of the transportation among the players. Fragnelli et al. (Math Methods Oper Res 52: 251-264, 2000) introduce the class of shortest path games and show it 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 five characterizations of the Shapley value (Hart and Mas-Colell's in Econometrica 57:589-614, 1989; Shapley's in Contributions to the theory of games II, annals of mathematics studies, vol 28. Princeton University Press, Princeton, pp 307-317, 1953; Young's in Int J Game Theory 14:65-72, 1985, Chun's in Games Econ Behav 45:119-130, 1989; van den Brink's in Int J Game Theory 30:309-319, 2001 axiomatizations), and conclude that all the mentioned axiomatizations are valid for the shortest path games. Fragnelli et al. (Math Methods Oper Res 52:251-264, 2000)'s axioms are based on the graph behind the problem, in this paper we do not consider graph specific axioms, we take axioms only, that is we consider all shortest path problems and we take the viewpoint of an abstract decision maker who focuses rather on the abstract problem than on the concrete situations.

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