American Institute of Mathematical Sciences

Advanced
October  2008, 4(4): 843-859. doi: 10.3934/jimo.2008.4.843

Price and delivery-time competition of perishable products: Existence and uniqueness of Nash equilibrium

Xiaolin Xu 1, and  Xiaoqiang Cai 2,

1. 

School of Business, Nanjing University, 210093, Nanjing, China
2. 

Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China

Received  April 2008 Revised  August 2008 Published  November 2008

We consider such a problem: Multiple sellers sell a family of substitutable perishable products in a common market with correlative random demands. Due to the perishable nature of a product, delivery time directly affects its freshness level, which in turn affects its demand. Each seller's demand is formulated as a function of all sellers' prices and delivery-times. To maximize his own expected profit, each seller needs to set his selling price and delivery time simultaneously, by taking into account his competitors' reactions. We present three models to address different practical situations. In Model I, we assume that each seller faces constant operating and purchasing costs, but is subject to a given service reliability constraint. In contrast, we assume delivery-time dependent operating and purchasing costs without service reliability constraints in Model II and Model III respectively. We establish the existence of a price and delivery-time equilibrium, under mild conditions in Model I and II, and restrictive conditions in Model III. A novel method is adopted to establish the uniqueness of the equilibrium in Model I, and an iterative procedure is designed to compute the equilibrium prices and delivery-times in Model III.
Keywords: price and delivery., Perishable product, Nash equilibrium.
Mathematics Subject Classification: Primary: 91A10, 91A4.
Citation: Xiaolin Xu, Xiaoqiang Cai. Price and delivery-time competition of perishable products: Existence and uniqueness of Nash equilibrium. Journal of Industrial & Management Optimization, 2008, 4 (4) : 843-859. doi: 10.3934/jimo.2008.4.843
[1]

Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics & Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006
[2]

Jian Hou, Liwei Zhang. A barrier function method for generalized Nash equilibrium problems. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1091-1108. doi: 10.3934/jimo.2014.10.1091
[3]

Yanhong Yuan, Hongwei Zhang, Liwei Zhang. A penalty method for generalized Nash equilibrium problems. Journal of Industrial & Management Optimization, 2012, 8 (1) : 51-65. doi: 10.3934/jimo.2012.8.51
[4]

Elvio Accinelli, Bruno Bazzano, Franco Robledo, Pablo Romero. Nash Equilibrium in evolutionary competitive models of firms and workers under external regulation. Journal of Dynamics & Games, 2015, 2 (1) : 1-32. doi: 10.3934/jdg.2015.2.1
[5]

Dean A. Carlson. Finding open-loop Nash equilibrium for variational games. Conference Publications, 2005, 2005 (Special) : 153-163. doi: 10.3934/proc.2005.2005.153
[6]

Shunfu Jin, Haixing Wu, Wuyi Yue, Yutaka Takahashi. Performance evaluation and Nash equilibrium of a cloud architecture with a sleeping mechanism and an enrollment service. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2407-2424. doi: 10.3934/jimo.2019060
[7]

Enkhbat Rentsen, Battur Gompil. Generalized Nash equilibrium problem based on malfatti's problem. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 209-220. doi: 10.3934/naco.2020022
[8]

Xiaona Fan, Li Jiang, Mengsi Li. Homotopy method for solving generalized Nash equilibrium problem with equality and inequality constraints. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1795-1807. doi: 10.3934/jimo.2018123
[9]

Shaokun Tao, Xianjin Du, Suresh P. Sethi, Xiuli He, Yu Li. Equilibrium decisions on pricing and innovation that impact reference price dynamics. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021157
[10]

Fatemeh Kangi, Seyed Hamid Reza Pasandideh, Esmaeil Mehdizadeh, Hamed Soleimani. The optimization of a multi-period multi-product closed-loop supply chain network with cross-docking delivery strategy. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021118
[11]

Rui Mu, Zhen Wu. Nash equilibrium points of recursive nonzero-sum stochastic differential games with unbounded coefficients and related multiple\\ dimensional BSDEs. Mathematical Control & Related Fields, 2017, 7 (2) : 289-304. doi: 10.3934/mcrf.2017010
[12]

Mei Ju Luo, Yi Zeng Chen. Smoothing and sample average approximation methods for solving stochastic generalized Nash equilibrium problems. Journal of Industrial & Management Optimization, 2016, 12 (1) : 1-15. doi: 10.3934/jimo.2016.12.1
[13]

Yanhong Yuan, Hongwei Zhang, Liwei Zhang. A smoothing Newton method for generalized Nash equilibrium problems with second-order cone constraints. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 1-18. doi: 10.3934/naco.2012.2.1
[14]

Bin Zhou, Hailin Sun. Two-stage stochastic variational inequalities for Cournot-Nash equilibrium with risk-averse players under uncertainty. Numerical Algebra, Control & Optimization, 2020, 10 (4) : 521-535. doi: 10.3934/naco.2020049
[15]

Po-Chung Yang, Hui-Ming Wee, Shen-Lian Chung, Yong-Yan Huang. Pricing and replenishment strategy for a multi-market deteriorating product with time-varying and price-sensitive demand. Journal of Industrial & Management Optimization, 2013, 9 (4) : 769-787. doi: 10.3934/jimo.2013.9.769
[16]

Ru Li, Guolin Yu. Strict efficiency of a multi-product supply-demand network equilibrium model. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2203-2215. doi: 10.3934/jimo.2020065
[17]

Carey Caginalp, Gunduz Caginalp. Asset price volatility and price extrema. Discrete & Continuous Dynamical Systems - B, 2020, 25 (5) : 1935-1958. doi: 10.3934/dcdsb.2020010
[18]

Janos Kollar. The Nash conjecture for threefolds. Electronic Research Announcements, 1998, 4: 63-73.

[19]

Yannick Viossat. Game dynamics and Nash equilibria. Journal of Dynamics & Games, 2014, 1 (3) : 537-553. doi: 10.3934/jdg.2014.1.537
[20]

William Geller, Bruce Kitchens, Michał Misiurewicz. Microdynamics for Nash maps. Discrete & Continuous Dynamical Systems, 2010, 27 (3) : 1007-1024. doi: 10.3934/dcds.2010.27.1007

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (66)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy