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.