American Institute of Mathematical Sciences

Advanced
  • 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

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 & 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), (1971), 90.   Google Scholar

[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.  doi: 10.1287/msom.2.4.410.12339.  Google Scholar

[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.  doi: 10.3934/jimo.2006.2.297.  Google Scholar

[4]

P. L. Brockett and L. L. Golden, A class of utility functions containing all the common utility functions,, Management Science, 33 (1987), 955.  doi: 10.1287/mnsc.33.8.955.  Google Scholar

[5]

G. P. Cachon, Supply chain coordination with contracts,, in Handbooks in Operations Research and Management Science, (2003), 227.  doi: 10.1016/S0927-0507(03)11006-7.  Google Scholar

[6]

X. Chen, M. Sim, D. S. Levi and P. Sun, Risk aversion in inventory management,, Operations Research, 55 (2007), 828.  doi: 10.1287/opre.1070.0429.  Google Scholar

[7]

L. Eeckhoudt, C. Gollier and H. Schlesinger, The risk-averse (and prudent) newsboy,, Management Science, 41 (1995), 786.  doi: 10.1287/mnsc.41.5.786.  Google Scholar

[8]

D. Fudenberg and J. Tirole, Game Theory,, MIT Press, (1991).   Google Scholar

[9]

I. Friend and M. E. Blume, The demand for risky assets,, The American Economic Review, 65 (1975), 900.   Google Scholar

[10]

A. Gasparro and J. Beckerman, Whole foods again lowers sales projections; specialty supermarket reports 6, Wall Street Journal (Online), (2014).   Google Scholar

[11]

K. Girotra and S. Netessine, How to build risk into your business model,, Harvard Business Review, 89 (2011), 100.   Google Scholar

[12]

C. A. Holt and S. K. Laury, Risk aversion and incentive effects,, American Economic Review, 92 (2002), 1644.  doi: 10.1257/000282802762024700.  Google Scholar

[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, (2012).   Google Scholar

[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.  doi: 10.1111/j.1467-8489.1982.tb00414.x.  Google Scholar

[15]

B. Keren and J. S. Pliskin, A benchmark solution for the risk-averse newsvendor problem,, European Journal of Operational Research, 174 (2006), 1643.  doi: 10.1016/j.ejor.2005.03.047.  Google Scholar

[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.  doi: 10.1016/S0305-0483(99)00017-1.  Google Scholar

[17]

S. A. Lippman and K. F. McCardle, The competitive newsboy,, Operations Research, 45 (1997), 54.  doi: 10.1287/opre.45.1.54.  Google Scholar

[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.  doi: 10.1016/j.ijpe.2012.08.017.  Google Scholar

[19]

J. W. Pratt, Risk aversion in the small and in the large,, Econometrica, 32 (1964), 122.   Google Scholar

[20]

M. Parlar, Game theoretic analysis of the substitutable product inventory problem with random demand,, Naval Research Logistics, 35 (1988), 397.  doi: 10.1002/1520-6750(198806)35:3<397::AID-NAV3220350308>3.0.CO;2-Z.  Google Scholar

[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.  doi: 10.1016/j.ejor.2010.11.024.  Google Scholar

[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.  doi: 10.2307/1243619.  Google Scholar

[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.  doi: 10.1287/mnsc.46.3.404.12070.  Google Scholar

[24]

F. W. Siegel and J. P. Hoban, Relative risk aversion revisited,, The Review of Economics and Statistics, 64 (1982), 481.  doi: 10.2307/1925947.  Google Scholar

[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.  doi: 10.1016/j.ejor.2003.08.065.  Google Scholar

[26]

H. B. Wolfe, A model for control of style merchandise,, Industrial Management Review, 9 (1968), 69.   Google Scholar

[27]

C. X. Wang, The loss-averse newsvendor game,, International Journal of Production Economics, 124 (2010), 448.  doi: 10.1016/j.ijpe.2009.12.007.  Google Scholar

[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.  doi: 10.1016/j.ejor.2008.04.002.  Google Scholar

[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.  doi: 10.1080/0003684042000280580.  Google Scholar

[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.  doi: 10.1016/j.ijpe.2014.05.009.  Google Scholar

[31]

Y. Z. Wang and Y. Gerchak, Supply chain coordination when demand is shelf-space dependent,, Manufacturing & Service Operations Management, 3 (2001), 82.  doi: 10.1287/msom.3.1.82.9998.  Google Scholar

[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.  doi: 10.3934/jimo.2015.11.515.  Google Scholar

[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.  doi: 10.1016/j.ijpe.2008.01.006.  Google Scholar

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), (1971), 90.   Google Scholar

[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.  doi: 10.1287/msom.2.4.410.12339.  Google Scholar

[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.  doi: 10.3934/jimo.2006.2.297.  Google Scholar

[4]

P. L. Brockett and L. L. Golden, A class of utility functions containing all the common utility functions,, Management Science, 33 (1987), 955.  doi: 10.1287/mnsc.33.8.955.  Google Scholar

[5]

G. P. Cachon, Supply chain coordination with contracts,, in Handbooks in Operations Research and Management Science, (2003), 227.  doi: 10.1016/S0927-0507(03)11006-7.  Google Scholar

[6]

X. Chen, M. Sim, D. S. Levi and P. Sun, Risk aversion in inventory management,, Operations Research, 55 (2007), 828.  doi: 10.1287/opre.1070.0429.  Google Scholar

[7]

L. Eeckhoudt, C. Gollier and H. Schlesinger, The risk-averse (and prudent) newsboy,, Management Science, 41 (1995), 786.  doi: 10.1287/mnsc.41.5.786.  Google Scholar

[8]

D. Fudenberg and J. Tirole, Game Theory,, MIT Press, (1991).   Google Scholar

[9]

I. Friend and M. E. Blume, The demand for risky assets,, The American Economic Review, 65 (1975), 900.   Google Scholar

[10]

A. Gasparro and J. Beckerman, Whole foods again lowers sales projections; specialty supermarket reports 6, Wall Street Journal (Online), (2014).   Google Scholar

[11]

K. Girotra and S. Netessine, How to build risk into your business model,, Harvard Business Review, 89 (2011), 100.   Google Scholar

[12]

C. A. Holt and S. K. Laury, Risk aversion and incentive effects,, American Economic Review, 92 (2002), 1644.  doi: 10.1257/000282802762024700.  Google Scholar

[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, (2012).   Google Scholar

[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.  doi: 10.1111/j.1467-8489.1982.tb00414.x.  Google Scholar

[15]

B. Keren and J. S. Pliskin, A benchmark solution for the risk-averse newsvendor problem,, European Journal of Operational Research, 174 (2006), 1643.  doi: 10.1016/j.ejor.2005.03.047.  Google Scholar

[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.  doi: 10.1016/S0305-0483(99)00017-1.  Google Scholar

[17]

S. A. Lippman and K. F. McCardle, The competitive newsboy,, Operations Research, 45 (1997), 54.  doi: 10.1287/opre.45.1.54.  Google Scholar

[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.  doi: 10.1016/j.ijpe.2012.08.017.  Google Scholar

[19]

J. W. Pratt, Risk aversion in the small and in the large,, Econometrica, 32 (1964), 122.   Google Scholar

[20]

M. Parlar, Game theoretic analysis of the substitutable product inventory problem with random demand,, Naval Research Logistics, 35 (1988), 397.  doi: 10.1002/1520-6750(198806)35:3<397::AID-NAV3220350308>3.0.CO;2-Z.  Google Scholar

[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.  doi: 10.1016/j.ejor.2010.11.024.  Google Scholar

[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.  doi: 10.2307/1243619.  Google Scholar

[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.  doi: 10.1287/mnsc.46.3.404.12070.  Google Scholar

[24]

F. W. Siegel and J. P. Hoban, Relative risk aversion revisited,, The Review of Economics and Statistics, 64 (1982), 481.  doi: 10.2307/1925947.  Google Scholar

[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.  doi: 10.1016/j.ejor.2003.08.065.  Google Scholar

[26]

H. B. Wolfe, A model for control of style merchandise,, Industrial Management Review, 9 (1968), 69.   Google Scholar

[27]

C. X. Wang, The loss-averse newsvendor game,, International Journal of Production Economics, 124 (2010), 448.  doi: 10.1016/j.ijpe.2009.12.007.  Google Scholar

[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.  doi: 10.1016/j.ejor.2008.04.002.  Google Scholar

[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.  doi: 10.1080/0003684042000280580.  Google Scholar

[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.  doi: 10.1016/j.ijpe.2014.05.009.  Google Scholar

[31]

Y. Z. Wang and Y. Gerchak, Supply chain coordination when demand is shelf-space dependent,, Manufacturing & Service Operations Management, 3 (2001), 82.  doi: 10.1287/msom.3.1.82.9998.  Google Scholar

[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.  doi: 10.3934/jimo.2015.11.515.  Google Scholar

[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.  doi: 10.1016/j.ijpe.2008.01.006.  Google Scholar

[1]

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 & Management Optimization, 2018, 14 (4) : 1397-1422. doi: 10.3934/jimo.2018013
[2]

Xiulan Wang, Yanfei Lan, Wansheng Tang. An uncertain wage contract model for risk-averse worker under bilateral moral hazard. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1815-1840. doi: 10.3934/jimo.2017020
[3]

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
[4]

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 & Management Optimization, 2018, 14 (2) : 687-705. doi: 10.3934/jimo.2017069
[5]

Wei Liu, Shiji Song, Ying Qiao, Han Zhao. The loss-averse newsvendor problem with random supply capacity. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1417-1429. doi: 10.3934/jimo.2016080
[6]

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 & Management Optimization, 2019, 15 (3) : 1289-1315. doi: 10.3934/jimo.2018096
[7]

Ganfu Wang, Xingzheng Ai, Chen Zheng, Li Zhong. Strategic inventory under suppliers competition. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-15. doi: 10.3934/jimo.2019048
[8]

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
[9]

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
[10]

Alain Bensoussan, Metin Çakanyildirim, Suresh P. Sethi. Censored newsvendor model revisited with unnormalized probabilities. Journal of Industrial & Management Optimization, 2009, 5 (2) : 391-402. doi: 10.3934/jimo.2009.5.391
[11]

Yeong-Cheng Liou, Siegfried Schaible, Jen-Chih Yao. Supply chain inventory management via a Stackelberg equilibrium. Journal of Industrial & Management Optimization, 2006, 2 (1) : 81-94. doi: 10.3934/jimo.2006.2.81
[12]

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
[13]

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
[14]

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, 2017, 13 (5) : 1-18. doi: 10.3934/jimo.2019060
[15]

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
[16]

Ruopeng Wang, Jinting Wang, Chang Sun. Optimal pricing and inventory management for a loss averse firm when facing strategic customers. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1521-1544. doi: 10.3934/jimo.2018019
[17]

Sanjoy Kumar Paul, Ruhul Sarker, Daryl Essam. Managing risk and disruption in production-inventory and supply chain systems: A review. Journal of Industrial & Management Optimization, 2016, 12 (3) : 1009-1029. doi: 10.3934/jimo.2016.12.1009
[18]

Filipe Martins, Alberto A. Pinto, Jorge Passamani Zubelli. Nash and social welfare impact in an international trade model. Journal of Dynamics & Games, 2017, 4 (2) : 149-173. doi: 10.3934/jdg.2017009
[19]

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
[20]

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

2018 Impact Factor: 1.025

Tools

Metrics

  • PDF downloads (25)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences