The envy-free pricing problem, unit-demand markets and connections with the network pricing problem
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- 作者：Cristina G. Fernandesa ; cris@ime.usp.br" class="auth_mail" title="E-mail the corresponding author ; Carlos E. Ferreiraa ; cef@ime.usp.br" class="auth_mail" title="E-mail the corresponding author ; Á ; lvaro J.P. Francob ; alvaro.junio@ufsc.br" class="auth_mail" title="E-mail the corresponding author ; Rafael C.S. Schoueryc ; schouery@ic.unicamp.br" class="auth_mail" title="E-mail the corresponding author
- 关键词：Pricing problems ; Envy-free allocations ; Unit-demand auctions
- 刊名：Discrete Optimization
- 出版年：2016
- 出版时间：November 2016
- 年：2016
- 卷：22
- 期：part_PA
- 页码：141-161
- 全文大小：870 K
文摘
A common problem faced in economics is to decide the pricing of products of a company, since poorly chosen prices might lead to low profit. One important model for this is the unit-demand envy-free pricing problem, in which one considers that every consumer buys an item that maximizes his own profit, and the goal is to find a pricing of the items that maximizes the expected profit of the seller. This is a practical and interesting problem which is, unfortunately, not in 
unless . We present two new MIP formulations for this problem and experimentally compare them to previous ones from the literature. We describe three models to generate different random instances for general unit-demand auctions, that we designed for the computational experiments. Each model has a nice economic interpretation. Our results show that one of our MIP formulations can sometimes lead to better results than the previous ones from the literature. We also consider a variant of the network pricing problem in which one has to price toll arcs in a highway, and prove that it is as hard to approximate as the envy-free pricing problem.
unless . We present two new MIP formulations for this problem and experimentally compare them to previous ones from the literature. We describe three models to generate different random instances for general unit-demand auctions, that we designed for the computational experiments. Each model has a nice economic interpretation. Our results show that one of our MIP formulations can sometimes lead to better results than the previous ones from the literature. We also consider a variant of the network pricing problem in which one has to price toll arcs in a highway, and prove that it is as hard to approximate as the envy-free pricing problem.