Mathematical Modeling And Algorithm Based On Game Theory In Network Location Problem

With the development of global economy,the market trend of network structure is more and more obvious,and the location of enterprise facilities is also gradually focused on the study of network location.Since the network location problem usually belongs to the category of discrete location,the problem has been transformed into an integer programming model to study.However,the introduction of the concept of game theory has changed people's traditional understanding of the network location,whose research involves more and more extensive,more and more profound theory.Therefore,how to use the game theory to study the market network location,which is the important strategic decision-making issues related to the operation of the enterprise and the entire market.In this paper,we focus on the market network location under cooperation or competition with complete or incomplete information and discuss the following issues:1.Study the Shapley-value location model based on network cooperative games.Two different Shapley-value location indexes are established by constructing characteristic functions based on the influential range and the influential degree.At the same time,the polynomial time algorithms for solving these models are obtained by theoretical derivations and proofs.2.Discuss the two-stage Cournot game model of the competitive location with complete information.A two-stage Cournot game model is established for the Cournot competition,which considers the strategies of location,production and sales.The paper designs the algorithm for solving the sub-game perfect Nash equilibrium,and a numerical example is given to show the rationality of the model and the effectiveness of the algorithm.3.Explore the Stackelberg-Cournot model of the competitive location with incomplete information.On the basis of the two-stage game,the Cournot competition of incomplete information between the incumbent and the entering enterprises is transformed into a Stackelberg-Cournot model,which is essentially a discrete optimization problem under the Bayes-Nash equilibrium constraints.Through the design of simulated annealing algorithm,the efficiency of solving the model has been greatly improved.