Geodesic
On a dynamic traveling salesman problem
Contributions to game theory and management, Tome 10 (2017), pp. 326-338

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In this paper we consider a dynamic traveling salesman problem (DTSP) in which $n$ objects (the salesman and $m$ customers) move on a plane with constant velocities. Each customer aims to meet the salesman as soon as possible. In turn, the salesman aspires to meet all customers for the minimal time. We formalize this problem as non-zero sum game of pursuit and find its solution as a Nash equilibrium. Finally, we give some examples to illustrate the obtained results.
Keywords: dynamic traveling salesman problem, non-zero sum game, Nash equilibrium. 
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     author = {Svetlana Tarashnina and Yaroslavna Pankratova and Aleksandra Purtyan},
     title = {On a dynamic traveling salesman problem},
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     pages = {326--338},
     publisher = {mathdoc},
     volume = {10},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2017_10_a19/}
}
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Svetlana Tarashnina; Yaroslavna Pankratova; Aleksandra Purtyan. On a dynamic traveling salesman problem. Contributions to game theory and management, Tome 10 (2017), pp. 326-338. http://geodesic.mathdoc.fr/item/CGTM_2017_10_a19/