The risk-averse newsvendor game with competition on demand

Previous Article
An interior-point $l_{\frac{1}{2}}$-penalty method for inequality constrained nonlinear optimization
JIMO Home
This Issue
Next Article
Two bounds for integrating the virtual dynamic cellular manufacturing problem into supply chain management

July 2016, 12(3): 931-947. doi: 10.3934/jimo.2016.12.931

The risk-averse newsvendor game with competition on demand

Yuwei Shen ^1, , Jinxing Xie ^1, and Tingting Li ^2,

1.	Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China, China
2.	School of Management Science and Engineering, Dongbei University of Finance and Economics, Dalian, 116025, China

Received July 2014 Revised April 2015 Published September 2015

Abstract
Related Papers

This paper studies the effect of risk-aversion in the competitive newsvendor game. Multiple newsvendors with risk-averse preferences face a random demand and the demand is allocated proportionally to their inventory levels. Each newsvendor aims to maximize his expected utility instead of his expected profit. Assuming a general form of risk-averse utility function, we prove that there exists a pure Nash equilibrium in this game, and it is also unique under certain conditions. We find that the order quantity of each newsvendor is decreasing in the degree of risk-aversion and increasing in the initial wealth. Newsvendors with moderate preferences of risk-aversion make more profits compared with the risk-neutral situation. We also discuss the joint effect of risk-aversion and competition. If the effect of risk-aversion is strong enough to dominate the effect of competition, the total inventory level under competition will be lower than that under centralized decision-making.

Keywords: competition, Inventory, newsvendor model, risk-averse, Nash equilibrium..

Mathematics Subject Classification: Primary: 90B05; Secondary: 91A8.

Citation: Yuwei Shen, Jinxing Xie, Tingting Li. The risk-averse newsvendor game with competition on demand. Journal of Industrial and Management Optimization, 2016, 12 (3) : 931-947. doi: 10.3934/jimo.2016.12.931

References:

[1]	K. J. Arrow, The theory of risk aversion, in Essays in the Theory of Risk-Bearing (ed. K. J. Arrow), Markham Publishing Company, 1971, 90-120.
[2]	V. Agrawal and S. Seshadri, Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem, Manufacturing & Service Operations Management, 2 (2000), 410-423. doi: 10.1287/msom.2.4.410.12339.
[3]	A. O. Brown and C. S. Tang, The impact of alternative performance measures on single-period inventory policy, Journal of Industrial and Management Optimization, 2 (2006), 297-318. doi: 10.3934/jimo.2006.2.297.
[4]	P. L. Brockett and L. L. Golden, A class of utility functions containing all the common utility functions, Management Science, 33 (1987), 955-964. doi: 10.1287/mnsc.33.8.955.
[5]	G. P. Cachon, Supply chain coordination with contracts, in Handbooks in Operations Research and Management Science, Vol. 11 (eds. S. C. Graves and A. G. de Kok), Elsevier, 2003, 227-339. doi: 10.1016/S0927-0507(03)11006-7.
[6]	X. Chen, M. Sim, D. S. Levi and P. Sun, Risk aversion in inventory management, Operations Research, 55 (2007), 828-842. doi: 10.1287/opre.1070.0429.
[7]	L. Eeckhoudt, C. Gollier and H. Schlesinger, The risk-averse (and prudent) newsboy, Management Science, 41 (1995), 786-794. doi: 10.1287/mnsc.41.5.786.
[8]	D. Fudenberg and J. Tirole, Game Theory, MIT Press, London, 1991.
[9]	I. Friend and M. E. Blume, The demand for risky assets, The American Economic Review, 65 (1975), 900-922.
[10]	A. Gasparro and J. Beckerman, Whole foods again lowers sales projections; specialty supermarket reports 6 Wall Street Journal (Online), 30 Jul 2014. Available from: http://search.proquest.com/docview/1549531450?accountid=14426.
[11]	K. Girotra and S. Netessine, How to build risk into your business model, Harvard Business Review, 89 (2011), 100-105.
[12]	C. A. Holt and S. K. Laury, Risk aversion and incentive effects, American Economic Review, 92 (2002), 1644-1655. doi: 10.1257/000282802762024700.
[13]	J. R. Hagerty, 3M begins untangling its 'hairballs' - making plastic hooks is harder than it seems; streamlining a four-state, 1,300-mile supply chain, Wall Street Journal, 17 May 2012. Available from: http://search.proquest.com/docview/1013910634?accountid=14426.
[14]	K. B. Hamal and J. R. Anderson, A note on decreasing absolute risk aversion among farmers in Nepal, Australian Journal of Agricultural Economics, 26 (1982), 220-225. doi: 10.1111/j.1467-8489.1982.tb00414.x.
[15]	B. Keren and J. S. Pliskin, A benchmark solution for the risk-averse newsvendor problem, European Journal of Operational Research, 174 (2006), 1643-1650. doi: 10.1016/j.ejor.2005.03.047.
[16]	M. Khouja, The single-period (news-vendor) problem: literature review and suggestions for future research, Omega-The International Journal of Management Science, 27 (1999), 537-553. doi: 10.1016/S0305-0483(99)00017-1.
[17]	S. A. Lippman and K. F. McCardle, The competitive newsboy, Operations Research, 45 (1997), 54-65. doi: 10.1287/opre.45.1.54.
[18]	W. Liu, S. J. Song and C. Wu, Impact of loss aversion on the newsvendor game with product substitution, International Journal of Production Economics, 141 (2013), 352-359. doi: 10.1016/j.ijpe.2012.08.017.
[19]	J. W. Pratt, Risk aversion in the small and in the large, Econometrica, 32 (1964), 122-136.
[20]	M. Parlar, Game theoretic analysis of the substitutable product inventory problem with random demand, Naval Research Logistics, 35 (1988), 397-409. doi: 10.1002/1520-6750(198806)35:3<397::AID-NAV3220350308>3.0.CO;2-Z.
[21]	Y. Qin, R. X. Wang, A. J. Vakhria, Y. W. Chen and M. M. H. Seref, The newsvendor problem: review and directions for future research, European Journal of Operational Research, 213 (2011), 361-374. doi: 10.1016/j.ejor.2010.11.024.
[22]	A. Saha, C. R. Shumway and H. Talpaz, Joint estimation of risk preference structure and technology using expo-power utility, American Journal of Agricultural Economics, 76 (1994), 173-184. doi: 10.2307/1243619.
[23]	M. E. Schweitzer and G. P. Cachon, Decision bias in the newsvendor problem with a known demand distribution: Experimental evidence, Management Science, 46 (2000), 404-420. doi: 10.1287/mnsc.46.3.404.12070.
[24]	F. W. Siegel and J. P. Hoban, Relative risk aversion revisited, The Review of Economics and Statistics, 64 (1982), 481-487. doi: 10.2307/1925947.
[25]	T. L. Urban, Inventory models with inventory-level-dependent demand: A comprehensive review and unifying theory, European Journal of Operational Research, 162 (2005), 792-804. doi: 10.1016/j.ejor.2003.08.065.
[26]	H. B. Wolfe, A model for control of style merchandise, Industrial Management Review, 9 (1968), 69-82.
[27]	C. X. Wang, The loss-averse newsvendor game, International Journal of Production Economics, 124 (2010), 448-452. doi: 10.1016/j.ijpe.2009.12.007.
[28]	C. X. Wang, S. Webster and N. C. Suresh, Would a risk-averse newsvendor order less at a higher selling price?, European Journal of Operational Research, 196 (2009), 544-553. doi: 10.1016/j.ejor.2008.04.002.
[29]	M. Wik, T. A. Kebede, O. Bergland and S. T. Holden, On the measurement of risk aversion from experimental data, Applied Economics, 36 (2004), 2443-2451. doi: 10.1080/0003684042000280580.
[30]	M. Wu, S. X. Zhu and R. H. Teunter, A risk-averse competitive newsvendor problem under the CVaR criterion, International Journal of Production Economics, 156 (2014), 13-23. doi: 10.1016/j.ijpe.2014.05.009.
[31]	Y. Z. Wang and Y. Gerchak, Supply chain coordination when demand is shelf-space dependent, Manufacturing & Service Operations Management, 3 (2001), 82-87. doi: 10.1287/msom.3.1.82.9998.
[32]	G. Xie, W. Y. Yue and S. Y. Wang, Optimal selection of cleaner products in a green supply chain with risk aversion, Journal of Industrial and Management Optimization, 11 (2015), 515-528. doi: 10.3934/jimo.2015.11.515.
[33]	T. J. Xiao and D. Q. Yang, Price and service competition of supply chains with risk-averse retailers under demand uncertainty, International Journal of Production Economics, 114 (2008), 187-200. doi: 10.1016/j.ijpe.2008.01.006.

show all references

References:

[1]	K. J. Arrow, The theory of risk aversion, in Essays in the Theory of Risk-Bearing (ed. K. J. Arrow), Markham Publishing Company, 1971, 90-120.
[2]	V. Agrawal and S. Seshadri, Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem, Manufacturing & Service Operations Management, 2 (2000), 410-423. doi: 10.1287/msom.2.4.410.12339.
[3]	A. O. Brown and C. S. Tang, The impact of alternative performance measures on single-period inventory policy, Journal of Industrial and Management Optimization, 2 (2006), 297-318. doi: 10.3934/jimo.2006.2.297.
[4]	P. L. Brockett and L. L. Golden, A class of utility functions containing all the common utility functions, Management Science, 33 (1987), 955-964. doi: 10.1287/mnsc.33.8.955.
[5]	G. P. Cachon, Supply chain coordination with contracts, in Handbooks in Operations Research and Management Science, Vol. 11 (eds. S. C. Graves and A. G. de Kok), Elsevier, 2003, 227-339. doi: 10.1016/S0927-0507(03)11006-7.
[6]	X. Chen, M. Sim, D. S. Levi and P. Sun, Risk aversion in inventory management, Operations Research, 55 (2007), 828-842. doi: 10.1287/opre.1070.0429.
[7]	L. Eeckhoudt, C. Gollier and H. Schlesinger, The risk-averse (and prudent) newsboy, Management Science, 41 (1995), 786-794. doi: 10.1287/mnsc.41.5.786.
[8]	D. Fudenberg and J. Tirole, Game Theory, MIT Press, London, 1991.
[9]	I. Friend and M. E. Blume, The demand for risky assets, The American Economic Review, 65 (1975), 900-922.
[10]	A. Gasparro and J. Beckerman, Whole foods again lowers sales projections; specialty supermarket reports 6 Wall Street Journal (Online), 30 Jul 2014. Available from: http://search.proquest.com/docview/1549531450?accountid=14426.
[11]	K. Girotra and S. Netessine, How to build risk into your business model, Harvard Business Review, 89 (2011), 100-105.
[12]	C. A. Holt and S. K. Laury, Risk aversion and incentive effects, American Economic Review, 92 (2002), 1644-1655. doi: 10.1257/000282802762024700.
[13]	J. R. Hagerty, 3M begins untangling its 'hairballs' - making plastic hooks is harder than it seems; streamlining a four-state, 1,300-mile supply chain, Wall Street Journal, 17 May 2012. Available from: http://search.proquest.com/docview/1013910634?accountid=14426.
[14]	K. B. Hamal and J. R. Anderson, A note on decreasing absolute risk aversion among farmers in Nepal, Australian Journal of Agricultural Economics, 26 (1982), 220-225. doi: 10.1111/j.1467-8489.1982.tb00414.x.
[15]	B. Keren and J. S. Pliskin, A benchmark solution for the risk-averse newsvendor problem, European Journal of Operational Research, 174 (2006), 1643-1650. doi: 10.1016/j.ejor.2005.03.047.
[16]	M. Khouja, The single-period (news-vendor) problem: literature review and suggestions for future research, Omega-The International Journal of Management Science, 27 (1999), 537-553. doi: 10.1016/S0305-0483(99)00017-1.
[17]	S. A. Lippman and K. F. McCardle, The competitive newsboy, Operations Research, 45 (1997), 54-65. doi: 10.1287/opre.45.1.54.
[18]	W. Liu, S. J. Song and C. Wu, Impact of loss aversion on the newsvendor game with product substitution, International Journal of Production Economics, 141 (2013), 352-359. doi: 10.1016/j.ijpe.2012.08.017.
[19]	J. W. Pratt, Risk aversion in the small and in the large, Econometrica, 32 (1964), 122-136.
[20]	M. Parlar, Game theoretic analysis of the substitutable product inventory problem with random demand, Naval Research Logistics, 35 (1988), 397-409. doi: 10.1002/1520-6750(198806)35:3<397::AID-NAV3220350308>3.0.CO;2-Z.
[21]	Y. Qin, R. X. Wang, A. J. Vakhria, Y. W. Chen and M. M. H. Seref, The newsvendor problem: review and directions for future research, European Journal of Operational Research, 213 (2011), 361-374. doi: 10.1016/j.ejor.2010.11.024.
[22]	A. Saha, C. R. Shumway and H. Talpaz, Joint estimation of risk preference structure and technology using expo-power utility, American Journal of Agricultural Economics, 76 (1994), 173-184. doi: 10.2307/1243619.
[23]	M. E. Schweitzer and G. P. Cachon, Decision bias in the newsvendor problem with a known demand distribution: Experimental evidence, Management Science, 46 (2000), 404-420. doi: 10.1287/mnsc.46.3.404.12070.
[24]	F. W. Siegel and J. P. Hoban, Relative risk aversion revisited, The Review of Economics and Statistics, 64 (1982), 481-487. doi: 10.2307/1925947.
[25]	T. L. Urban, Inventory models with inventory-level-dependent demand: A comprehensive review and unifying theory, European Journal of Operational Research, 162 (2005), 792-804. doi: 10.1016/j.ejor.2003.08.065.
[26]	H. B. Wolfe, A model for control of style merchandise, Industrial Management Review, 9 (1968), 69-82.
[27]	C. X. Wang, The loss-averse newsvendor game, International Journal of Production Economics, 124 (2010), 448-452. doi: 10.1016/j.ijpe.2009.12.007.
[28]	C. X. Wang, S. Webster and N. C. Suresh, Would a risk-averse newsvendor order less at a higher selling price?, European Journal of Operational Research, 196 (2009), 544-553. doi: 10.1016/j.ejor.2008.04.002.
[29]	M. Wik, T. A. Kebede, O. Bergland and S. T. Holden, On the measurement of risk aversion from experimental data, Applied Economics, 36 (2004), 2443-2451. doi: 10.1080/0003684042000280580.
[30]	M. Wu, S. X. Zhu and R. H. Teunter, A risk-averse competitive newsvendor problem under the CVaR criterion, International Journal of Production Economics, 156 (2014), 13-23. doi: 10.1016/j.ijpe.2014.05.009.
[31]	Y. Z. Wang and Y. Gerchak, Supply chain coordination when demand is shelf-space dependent, Manufacturing & Service Operations Management, 3 (2001), 82-87. doi: 10.1287/msom.3.1.82.9998.
[32]	G. Xie, W. Y. Yue and S. Y. Wang, Optimal selection of cleaner products in a green supply chain with risk aversion, Journal of Industrial and Management Optimization, 11 (2015), 515-528. doi: 10.3934/jimo.2015.11.515.
[33]	T. J. Xiao and D. Q. Yang, Price and service competition of supply chains with risk-averse retailers under demand uncertainty, International Journal of Production Economics, 114 (2008), 187-200. doi: 10.1016/j.ijpe.2008.01.006.

[1]	Bin Zhou, Hailin Sun. Two-stage stochastic variational inequalities for Cournot-Nash equilibrium with risk-averse players under uncertainty. Numerical Algebra, Control and Optimization, 2020, 10 (4) : 521-535. doi: 10.3934/naco.2020049
[2]	Kegui Chen, Xinyu Wang, Min Huang, Wai-Ki Ching. Compensation plan, pricing and production decisions with inventory-dependent salvage value, and asymmetric risk-averse sales agent. Journal of Industrial and Management Optimization, 2018, 14 (4) : 1397-1422. doi: 10.3934/jimo.2018013
[3]	Bin Chen, Wenying Xie, Fuyou Huang, Juan He. Quality competition and coordination in a VMI supply chain with two risk-averse manufacturers. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2903-2924. doi: 10.3934/jimo.2020100
[4]	Xiulan Wang, Yanfei Lan, Wansheng Tang. An uncertain wage contract model for risk-averse worker under bilateral moral hazard. Journal of Industrial and Management Optimization, 2017, 13 (4) : 1815-1840. doi: 10.3934/jimo.2017020
[5]	Min Li, Jiahua Zhang, Yifan Xu, Wei Wang. Effects of disruption risk on a supply chain with a risk-averse retailer. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1365-1391. doi: 10.3934/jimo.2021024
[6]	Zhiyuan Zhen, Honglin Yang, Wenyan Zhuo. Financing and ordering decisions in a capital-constrained and risk-averse supply chain for the monopolist and non-monopolist supplier. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021104
[7]	Jie Jiang, Zhiping Chen, He Hu. Stability of a class of risk-averse multistage stochastic programs and their distributionally robust counterparts. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2415-2440. doi: 10.3934/jimo.2020075
[8]	Xiaolin Xu, Xiaoqiang Cai. Price and delivery-time competition of perishable products: Existence and uniqueness of Nash equilibrium. Journal of Industrial and Management Optimization, 2008, 4 (4) : 843-859. doi: 10.3934/jimo.2008.4.843
[9]	Yanju Zhou, Zhen Shen, Renren Ying, Xuanhua Xu. A loss-averse two-product ordering model with information updating in two-echelon inventory system. Journal of Industrial and Management Optimization, 2018, 14 (2) : 687-705. doi: 10.3934/jimo.2017069
[10]	Wei Liu, Shiji Song, Ying Qiao, Han Zhao. The loss-averse newsvendor problem with random supply capacity. Journal of Industrial and Management Optimization, 2017, 13 (3) : 1417-1429. doi: 10.3934/jimo.2016080
[11]	Ganfu Wang, Xingzheng Ai, Chen Zheng, Li Zhong. Strategic inventory under suppliers competition. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2159-2173. doi: 10.3934/jimo.2019048
[12]	Prasenjit Pramanik, Sarama Malik Das, Manas Kumar Maiti. Note on : Supply chain inventory model for deteriorating items with maximum lifetime and partial trade credit to credit risk customers. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1289-1315. doi: 10.3934/jimo.2018096
[13]	Nana Wan, Li Li, Xiaozhi Wu, Jianchang Fan. Risk minimization inventory model with a profit target and option contracts under spot price uncertainty. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021093
[14]	Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics and Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006
[15]	Jian Hou, Liwei Zhang. A barrier function method for generalized Nash equilibrium problems. Journal of Industrial and Management Optimization, 2014, 10 (4) : 1091-1108. doi: 10.3934/jimo.2014.10.1091
[16]	Yanhong Yuan, Hongwei Zhang, Liwei Zhang. A penalty method for generalized Nash equilibrium problems. Journal of Industrial and Management Optimization, 2012, 8 (1) : 51-65. doi: 10.3934/jimo.2012.8.51
[17]	Wei Liu, Shiji Song, Ying Qiao, Han Zhao, Huachang Wang. The loss-averse newsvendor problem with quantity-oriented reference point under CVaR criterion. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021085
[18]	Alain Bensoussan, Metin Çakanyildirim, Suresh P. Sethi. Censored newsvendor model revisited with unnormalized probabilities. Journal of Industrial and Management Optimization, 2009, 5 (2) : 391-402. doi: 10.3934/jimo.2009.5.391
[19]	Weiyi Zhang, Ling Zhou. Global asymptotic stability of constant equilibrium in a nonlocal diffusion competition model with free boundaries. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022062
[20]	Yeong-Cheng Liou, Siegfried Schaible, Jen-Chih Yao. Supply chain inventory management via a Stackelberg equilibrium. Journal of Industrial and Management Optimization, 2006, 2 (1) : 81-94. doi: 10.3934/jimo.2006.2.81

2020 Impact Factor: 1.801

Tools

Metrics

Other articles
by authors

on AIMS
Yuwei Shen Jinxing Xie Tingting Li
on Google Scholar
Yuwei Shen Jinxing Xie Tingting Li

[Back to Top]