On the core of traveling salesman games

We define excess rate to study the core of traveling salesman games from a perspective of optimization, propose a new variant of the traveling salesman problem, and build a link between the two problems. An exact formula for the lowest achievable excess rate is found, which explains the existence of core emptiness. We then develop an implementable method to check whether empty core exists in general case. The results apply for both symmetric and asymmetric traveling salesman games.

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