Mathematical Programming

, Volume 53, Issue 1–3, pp 199–211

# Traveling salesman games

• Jos A. M. Potters
• Imma J. Curiel
• Stef H. Tijs
Article

## 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.

### AMS 1980 Subject Classifications

Primary 90D12 Secondary 90C08

### Key words

Traveling salesman problem game theory

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### References

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© The Mathematical Programming Society, Inc. 1992

## Authors and Affiliations

• Jos A. M. Potters
• 1
• Imma J. Curiel
• 2
• Stef H. Tijs
• 1
1. 1.Department of MathematicsUniversity of Nijmegen, ToernooiveldNijmegenNetherlands
2. 2.Department of Mathematics and StatisticsUniversity of MarylandBaltimore County, CatonsvilleUSA