A Stochastic Knapsack Game: Revenue Management in Competitions

TL;DR

This paper introduces a stochastic knapsack game model for revenue management in competitive markets, combining dynamic recursive procedures with game theory to analyze seller behavior and establish structural properties.

Contribution

It develops a novel dynamic recursive framework integrating stochastic knapsack and game theory for competitive revenue management analysis.

Findings

Established a dynamic recursive procedure for the model

Proved fundamental structural properties of the game

Integrated value and utility functions in the analysis

Abstract

We study a mathematical model for revenue management under competition with multiple sellers. The model combines the stochastic knapsack problem, a classic revenue management model, with a non coorperative game model that characterizes the sellers' rational behavior. We are able to establish a dynamic recursive procedure that incorporate the value function with the utility function of the games. The formalization of the dynamic recursion allows us to establish some fundamental structural properties.