EQUILIBRIUM SOLUTION IN QUEUING GAMES PLAYED ON 3×3-GRID

Abstract

In this paper, we study the existence of equilibrium play in a specific classof queuing game played on a 3×3-gird as non-cooperative 2-players game. In this game,both players compete to select, from a set of paths available for each player, just one pathto use for their customers and exit from the grid after getting the required service as soon aspossible. Every node in this grid is a M=M=1 queue with dierent service rates. We discussthe existence of equilibrium strategies in two cases: first case, both players can share thesame entering and ending nodes. Second case, both players cannot share the same enteringand ending nodes. We compute the pay-off matrices for both players in two cases. Using anumerical calculation, we find the best reply and the equilibrium strategies for both playersif they have equal or unequal arrival rates. Also, the equilibrium play studied in which thereis a relation between these rates in this queuing game.