On the Core of Multiple Longest Traveling Salesman Games
CentER Discussion Paper No. 2003-127
18 Pages Posted: 16 Jul 2004
Date Written: 2003
In this paper, we introduce multiple longest traveling salesman (MLTS) games. An MLTS game arises from a network in which a salesman has to visit each node (player) precisely once, except its home location, in an order that maximizes the total reward. First, it is shown that the value of a coalition of an MLTS game is determined by taking the maximum of suitable combinations of one and two person coalitions. Secondly, it is shown that MLTS games with five or less players have a nonempty core. However, a six player MLTS game may have an empty core. For the special instance where the reward between a pair of nodes is equal to 0 or 1, we provide relations between the structure of the core and the underlying network.
Keywords: Game theory, longest traveling salesman problem/game, multiple longest traveling salesman problem/game, core
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