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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

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