A competitive many-period postman problem with varying parameters

Abstract

Let defined multistep game ΓG on a graph tree Γ. The postman’s problem on a complete graph with finite number of agents which responsible for the postman’s route and with varying weights given to the graph edges is a stage game G in each vertex on graph tree Γ. The problem G will be called a competitive one-period postman problem with varying parameters. In this parer competitive many-period postman problem with with varying papametres is examined. A multistep game with the postman problem realized on each step having a finite number of agents and varying matrix of weights given to the graph edges depending on the step (period), will be called a competitive many-period postman problem with varying parameters. The payoffs of the postman problem participants (players) including the postman himself in the simultaneous games G are their profits minus costs for providing postman’s movement on the routes. The routes are the players’ strategies. An algorithm for finding a compromise situation for solving simultaneous games is proposed. The theory is illustrated by the example of three-step game of three players. 7250 Xeniya Grigorieva and Oleg Malafeev Mathematics Subject Classification: 91 Axx

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