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We study a mathematical model for revenue management under competition withmultiple sellers. The model combines the stochastic knapsack problem, a classicrevenue management model, with a non coorperative game model that characterizesthe sellers' rational behavior. We are able to establish a dynamic recursiveprocedure that incorporate the value function with the utility function of thegames. The formalization of the dynamic recursion allows us to establish somefundamental structural properties.

A Stochastic Knapsack Game: Revenue Management in Competitions