The Study Of Pricing Model

We study the problems of pricing a product in a given social network.The goal is to maximize the revenue.The value of the product may be different for different consumers.The value is determined by two factors:intrinsic value of the product to the consumer and the variable externalities.A social network is a triple(G,?,?),where G is a graph,whose verties represent consumers,w:E(G)? R assigns to each edge uv a weight w(uv)which is the influence of u and v to each other.7:V(G)? R+ assigns to each vertex v a weight ?(v)which is the intrinsic value of the product for v.In the complete information networks,the intrinsic value and the variable ex-ternalities are known.Previous studies focus on negative or positive externalities in complete information networks.In this paper we study pricing model with both posi-tive and negative externalities.In Chapter 1,we introduce the background of pricing problems with externalities and the IPE-model.In Chapter 2,we show that it is NP-hard to find an optimal iterative pricing in the complete information networks.In addition,we prove:if the total consumers' intrinsic value is much larger than the total positive externalities,then the greedy algorithm is 2-approximation in general network.In Chapter 3,we prove that the revenue can be much lower than the maximal revenue if the pricing is limited to pricing sequences of length at most m for some constant m.In Chapter 4,we give the optimal strategies and revenues for the trivially weighted star network with uniform intrinsic value,and prove that there exists a single pricing that is a 2-approximation algorithm when the number of consumers is more than 4.We also prove:if uniform intrinsic value is not lower than 3,then there exists a single pricing that works well in the disjiont union of star networks.