Competitive and Cooperative Assortment Games under Markov Chain Choice Model

69 Pages Posted: 18 Jun 2020 Last revised: 30 Jun 2023

See all articles by Kameng Nip

Kameng Nip

Xiamen University

Changjun Wang

Beijing University of Technology

Zizhuo Wang

The Chinese University of Hong Kong, Shenzhen

Date Written: May 22, 2020

Abstract

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, i.e., an assortment to o er 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 on the assortments and the payoffs 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 o er a broader assortment in the equilibrium, which could include products that are not pro table in the monopolistic or the central planner setting, and it will eventually lead to a decrease of 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 how players presume other players' behavior. Interestingly, we find that when the players take a pessimistic view regarding the behavior of other players, 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 take an optimistic view regarding the behavior of other players, a stable coalition may not exist.

Keywords: Assortment Planning; Markov Chain Choice Model; Non-Cooperative Game; Cooperative Game

Suggested Citation

Nip, Kameng and Wang, Changjun and Wang, Zizhuo, Competitive and Cooperative Assortment Games under Markov Chain Choice Model (May 22, 2020). Available at SSRN: https://ssrn.com/abstract=3607722 or http://dx.doi.org/10.2139/ssrn.3607722

Kameng Nip (Contact Author)

Xiamen University ( email )

School of Mathematical Sciences
Xiamen, Fujian 361005
China

Changjun Wang

Beijing University of Technology ( email )

100 Ping Le Yuan
Chaoyang District
Beijing, Beijing 100020
China

Zizhuo Wang

The Chinese University of Hong Kong, Shenzhen ( email )

2001 Longxiang Road
Longgang District
Shenzhen, Guangdong 517182
China

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
156
Abstract Views
932
Rank
341,599
PlumX Metrics