# Traveling salesman games

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DOI: 10.1007/BF01585702

- Cite this article as:
- Potters, J.A.M., Curiel, I.J. & Tijs, S.H. Mathematical Programming (1992) 53: 199. doi:10.1007/BF01585702

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## Abstract

In this paper we discuss the problem of how to divide the total cost of a round trip along several institutes among the institutes visited. We introduce two types of cooperative games—fixed-route traveling salesman games and traveling salesman games—as a tool to attack this problem. Under very mild conditions we prove that fixed-route traveling salesman games have non-empty cores if the fixed route is a solution of the classical traveling salesman problem. Core elements provide us with fair cost allocations. A traveling salesman game may have an empty core, even if the cost matrix satisfies the triangle inequality. In this paper we introduce a class of matrices defining TS-games with non-empty cores.