Competitive and Cooperative Assortment Games under Markov Chain Choice Model

doi:10.1111/poms.13593

	Competitive and Cooperative Assortment Games under Markov Chain Choice Model
	Nip, Kameng 4; Wang, Changjun 3; Wang, Zizhuo 1,2
刊名	PRODUCTION AND OPERATIONS MANAGEMENT
	2021-11-26
页码	19
关键词	assortment planning Markov chain choice model non-cooperative game cooperative game
ISSN号	1059-1478
DOI	10.1111/poms.13593
英文摘要	In this work, we study the assortment planning games in which multiple retailers interact in the market. Each retailer owns some of the products and their goal is to select a subset of products, that is, an assortment to offer to the customers so as to maximize their expected revenue. The purchase behavior of the customer is assumed to follow the Markov chain choice model. We consider two types of assortment games under the Markov chain choice model-a competitive game and a cooperative game. In the assortment competition game, we show that there always exists a pure-strategy Nash equilibrium and such equilibrium can be found in polynomial time. We also identify an easy-to-check condition for the uniqueness of the Nash equilibrium. Then we analyze the equilibrium outcome of this competition game, and compare the outcome with that in a monopolistic setting and a central planner setting. We show that under the assortment competition game, each retailer will offer a broader assortment in the equilibrium, which could include products that are not profitable in the monopolistic or the central planner setting, and it will eventually lead to a decrease in revenue for each player. Furthermore, we show that the price-of-anarchy and the price-of-stability of the game can be arbitrarily large. Motivated by these results, we further consider the assortment cooperation game under the Markov chain choice model, in which retailers are allowed to form coalitions. We consider two settings of cooperative games distinguished by the way we assume other players' behaviors outside a coalition. Interestingly, we find that when the players are assumed to be intrinsically competitive (meaning that players outside a coalition are assumed to be a collection of competing players), then there is incentive for all the players to form a grand coalition and there exists an allocation of the total revenue that makes the coalition stable (exists a core to the game). However, when the players are assumed to be intrinsically collaborative (meaning that players outside a coalition are assumed to form another coalition), then a stable coalition may not exist.
资助项目	National Natural Science Foundation of China (NSFC)[NSFC-72150002] ; Natural Science Foundation of Fujian Province of China[2021J05011] ; Young Elite Scientists Sponsorship Program by CAST[2018QNRC001]
WOS研究方向	Engineering ; Operations Research & Management Science
语种	英语
出版者	WILEY
WOS记录号	WOS:000722565800001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59631]
专题	中国科学院数学与系统科学研究院
通讯作者	Nip, Kameng
作者单位	1.Shenzhen Res Inst Big Data, Shenzhen 518172, Peoples R China 2.Chinese Univ Hong Kong, Sch Data Sci, Shenzhen 518172, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China
推荐引用方式 GB/T 7714	Nip, Kameng,Wang, Changjun,Wang, Zizhuo. Competitive and Cooperative Assortment Games under Markov Chain Choice Model[J]. PRODUCTION AND OPERATIONS MANAGEMENT,2021:19.
APA	Nip, Kameng,Wang, Changjun,&Wang, Zizhuo.(2021).Competitive and Cooperative Assortment Games under Markov Chain Choice Model.PRODUCTION AND OPERATIONS MANAGEMENT,19.
MLA	Nip, Kameng,et al."Competitive and Cooperative Assortment Games under Markov Chain Choice Model".PRODUCTION AND OPERATIONS MANAGEMENT (2021):19.