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## How to share partial information with competitive manufacturers

 1 School of Management and Economics, Beijing Institute of Technology, Beijing, 100081, China, Springfield, MO 65801-2604, USA 2 School of Mathematical Sciences, Tiangong University, Tianjin 300387, China, Springfield, MO 65810, USA

*Corresponding author: Fujun Hou

Received  August 2021 Revised  December 2021 Early access January 2022

This paper investigates the partial information sharing of a supply chain including one retailer and two competitive manufacturers. The retailer has information about the uncertain market demand, and can share partial information with neither, one, or both of the manufacturers. We formulate three pricing decision models, and explore how some parameters (e.g., the amount of shared information, competition intensity, etc.) affect pricing and profits. Moreover, we give the sufficient conditions that each member benefits from the retailer's partial information sharing.

Citation: Huimin Zhang, Jing Zhao, Fujun Hou. How to share partial information with competitive manufacturers. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022010
##### References:
 [1] W. Bian, J. Shang and J. Zhang, Two-way information sharing under supply chain competition, International Journal of Production Economics, 178 (2016), 82-94.  doi: 10.1016/j.ijpe.2016.04.025. [2] K. Cai, S. He and Z. He, Information sharing under different warranty policies with cost sharing in supply chains, International Transactions in Operational Research, 27 (2020), 1550-1572.  doi: 10.1111/itor.12597. [3] W. H. J. Chu and C. C. Lee, Strategic information sharing in a supply chain, European Journal of Operational Research, 174 (2006), 1567-1579.  doi: 10.1016/j.ejor.2005.02.053. [4] R. Dominguez, S. Cannella, A. P. Barbosa-Póvoa and J. M. Framinan, OVAP: A strategy to implement partial information sharing among supply chain retailers, Transportation Research Part E, 110 (2018), 122-136.  doi: 10.1016/j.tre.2017.12.016. [5] E. Gal-Or, T. Geylani and A. J. Dukes, Information sharing in a channel with partially informed retailers, Marketing Science, 110 (2008), 642-658. [6] E. Gal-Or, Information sharing in oligopoly, Econometrica, 53 (1985), 329-343.  doi: 10.2307/1911239. [7] M. Ganesh, S. Raghunathan and C. Rajendran, Distribution and equitable sharing of value from information sharing within serial supply chains, IEEE Transactions on Engineering Management, 61 (2014), 225-236.  doi: 10.1109/TEM.2013.2271534. [8] M. Ganesh, S. Raghunathan and C. Rajendran, The value of information sharing in a multi-product, multi-level supply chain: Impact of product substitution, demand correlation, and partial information sharing, Decision Support Systems, 58 (2014), 79-94.  doi: 10.1016/j.dss.2013.01.012. [9] L. Guo, T. Li and H. Zhang, Strategic information sharing in competing channels, Production and Operations Management Society, 23 (2014), 1719-1731.  doi: 10.1111/poms.12195. [10] A. Y. Ha and S. Tong, Contracting and information sharing under supply chain competition, Management Science, 54 (2008), 701-715.  doi: 10.1287/mnsc.1070.0795. [11] A. Y. Ha, S. Tong and H. Zhang, Sharing demand information in competing supply chains with production diseconomies, Management Science, 57 (2011), 566-581.  doi: 10.1287/mnsc.1100.1295. [12] Y. S. Huang, J. S. Hung and J. W. Ho, A study on information sharing for supply chains with multiple suppliers, Computers & Industrial Engineering, 104 (2017), 114-123.  doi: 10.1016/j.cie.2016.12.014. [13] Y. S. Huang, M. C. Li and J. W. Ho, Determination of the optimal degree of information sharing in a two-echelon supply chain, International Journal of Production Research, 54 (2016), 1518-1534.  doi: 10.1080/00207543.2015.1092615. [14] B. Jiang, L. Tian, Y. Xu and F. Zhang, To share or not to share: Demand forecast sharing in a distribution channel, Marketing Science, 35 (2016), 1-10. [15] J. S. Lau, G. Q. Huang and K. L. Mak, Impact of information sharing on inventory replenishment in divergent supply chains, International Journal of Production Research, 42 (2004), 919-941.  doi: 10.1080/00207540310001628911. [16] M. Lei, H. Liu, H. Deng, T. Huang and G. K. Leong, Demand information sharing and channel choice in a dual-channel supply chain with multiple retailers, International Journal of Production Research, 52 (2014), 6792-6818.  doi: 10.1080/00207543.2014.918286. [17] L. Li, Cournot oligopoly with information sharing, RAND Journal of Economic, 16 (1985), 521-536.  doi: 10.2307/2555510. [18] L. Li, Information sharing in a supply chain with horizontal competition, Management Science, 48 (2002), 1196-1212. [19] T. Li and H. Zhang, Information sharing in a supply chain with a make-to-stock manufacturer, Omega, 50 (2015), 115-125.  doi: 10.1016/j.omega.2014.08.001. [20] L. Li and H. Zhang, Confidentially and information sharing in supply chain coordination, Management Science, 54 (2008), 1467-1481. [21] B. K. Mishra, S. Raghunathan and X. Yue, Demand forecast sharing in supply chains, Production and Operations Management, 18 (2009), 152-166.  doi: 10.1111/j.1937-5956.2009.01013.x. [22] M. Raith, A general model of information in oligopoly, Journal of Economic Theory, 71 (1996), 260-288. [23] N. Shamir and H. Shin, Public forecast information sharing in a market with competing supply chains, Management Science, 62 (2016), 2994-3022. [24] W. Shang, A. Y. Ha and S. Tong, Information sharing in a supply chain with a common retailer, Management Science, 62 (2016), 245-263.  doi: 10.1287/mnsc.2014.2127. [25] N. Shi, S. Zhou, F. Wang, S. Xu and S. Xiong, Horizontal cooperation and information sharing between suppliers in the manufacturer-supplier triad, International Journal of Production Research, 52 (2014), 4526-4547.  doi: 10.1080/00207543.2013.869630. [26] M. Shnaiderman and F. El Ouardighi, The impact of partial information sharing in a two-echelon supply chain, Operations Research Letters, 42 (2014), 234-237.  doi: 10.1016/j.orl.2014.03.006. [27] P. D. Tai, T. T. H. Duc and J. Buddhakulsomsiri, Value of information sharing in supply chain under promotional competition, International Transactions in Operational Research, (2020), 1–33. doi: 10.1111/itor.12859. [28] X. Vives, Duopoly information equilibrium: Cournot and Bertrand, Journal of Economic Theory, 34 (1984), 71-94.  doi: 10.1016/0022-0531(84)90162-5. [29] J. Wei, J. Zhao and X. Hou, Bilateral information sharing in two supply chains with complementary products, Applied Mathematical Modelling, 72 (2019), 28-49.  doi: 10.1016/j.apm.2019.03.015. [30] R. Yan and Z. Pei, Incentive information sharing in various market structures, Decision Support Systems, 76 (2015), 76-86.  doi: 10.1016/j.dss.2015.03.003. [31] X. Yue and J. Liu, Demand forecast sharing in a dual-channel supply chain, European Journal of Operational Research, 174 (2006), 646-667.  doi: 10.1016/j.ejor.2004.12.020. [32] H. Zhang, Vertical information exchange in a supply chain with duopoly retailers, Production and Operations Management, 11 (2002), 531-546.  doi: 10.1111/j.1937-5956.2002.tb00476.x. [33] T. Zhang, X. Zhu, C. Zhou and M. Liu, Pricing and advertising the relief goods under various information sharing scenarios, International Transactions in Operational Research, 24 (2017), 867-889.  doi: 10.1111/itor.12221. [34] J. Zhao, W. Tang, R. Zhao and J. Wei, Pricing decisions for substitutable products with a common retailer in fuzzy environments, European Journal of Operational Research, 216 (2012), 409-419.  doi: 10.1016/j.ejor.2011.07.026. [35] X. Zhao, L. Xue and F. Zhang, Outsourcing competition and information sharing with asymmetrically informed suppliers, Production and Operations Management, 23 (2014), 1706-1718. [36] M. Zhou, B. Dan, S. Ma and X. Zhang, Supply chain coordination with information sharing: The informational advantage of GPOs, European Journal of Operational Research, 256 (2017), 785-802.  doi: 10.1016/j.ejor.2016.06.045.

show all references

##### References:
 [1] W. Bian, J. Shang and J. Zhang, Two-way information sharing under supply chain competition, International Journal of Production Economics, 178 (2016), 82-94.  doi: 10.1016/j.ijpe.2016.04.025. [2] K. Cai, S. He and Z. He, Information sharing under different warranty policies with cost sharing in supply chains, International Transactions in Operational Research, 27 (2020), 1550-1572.  doi: 10.1111/itor.12597. [3] W. H. J. Chu and C. C. Lee, Strategic information sharing in a supply chain, European Journal of Operational Research, 174 (2006), 1567-1579.  doi: 10.1016/j.ejor.2005.02.053. [4] R. Dominguez, S. Cannella, A. P. Barbosa-Póvoa and J. M. Framinan, OVAP: A strategy to implement partial information sharing among supply chain retailers, Transportation Research Part E, 110 (2018), 122-136.  doi: 10.1016/j.tre.2017.12.016. [5] E. Gal-Or, T. Geylani and A. J. Dukes, Information sharing in a channel with partially informed retailers, Marketing Science, 110 (2008), 642-658. [6] E. Gal-Or, Information sharing in oligopoly, Econometrica, 53 (1985), 329-343.  doi: 10.2307/1911239. [7] M. Ganesh, S. Raghunathan and C. Rajendran, Distribution and equitable sharing of value from information sharing within serial supply chains, IEEE Transactions on Engineering Management, 61 (2014), 225-236.  doi: 10.1109/TEM.2013.2271534. [8] M. Ganesh, S. Raghunathan and C. Rajendran, The value of information sharing in a multi-product, multi-level supply chain: Impact of product substitution, demand correlation, and partial information sharing, Decision Support Systems, 58 (2014), 79-94.  doi: 10.1016/j.dss.2013.01.012. [9] L. Guo, T. Li and H. Zhang, Strategic information sharing in competing channels, Production and Operations Management Society, 23 (2014), 1719-1731.  doi: 10.1111/poms.12195. [10] A. Y. Ha and S. Tong, Contracting and information sharing under supply chain competition, Management Science, 54 (2008), 701-715.  doi: 10.1287/mnsc.1070.0795. [11] A. Y. Ha, S. Tong and H. Zhang, Sharing demand information in competing supply chains with production diseconomies, Management Science, 57 (2011), 566-581.  doi: 10.1287/mnsc.1100.1295. [12] Y. S. Huang, J. S. Hung and J. W. Ho, A study on information sharing for supply chains with multiple suppliers, Computers & Industrial Engineering, 104 (2017), 114-123.  doi: 10.1016/j.cie.2016.12.014. [13] Y. S. Huang, M. C. Li and J. W. Ho, Determination of the optimal degree of information sharing in a two-echelon supply chain, International Journal of Production Research, 54 (2016), 1518-1534.  doi: 10.1080/00207543.2015.1092615. [14] B. Jiang, L. Tian, Y. Xu and F. Zhang, To share or not to share: Demand forecast sharing in a distribution channel, Marketing Science, 35 (2016), 1-10. [15] J. S. Lau, G. Q. Huang and K. L. Mak, Impact of information sharing on inventory replenishment in divergent supply chains, International Journal of Production Research, 42 (2004), 919-941.  doi: 10.1080/00207540310001628911. [16] M. Lei, H. Liu, H. Deng, T. Huang and G. K. Leong, Demand information sharing and channel choice in a dual-channel supply chain with multiple retailers, International Journal of Production Research, 52 (2014), 6792-6818.  doi: 10.1080/00207543.2014.918286. [17] L. Li, Cournot oligopoly with information sharing, RAND Journal of Economic, 16 (1985), 521-536.  doi: 10.2307/2555510. [18] L. Li, Information sharing in a supply chain with horizontal competition, Management Science, 48 (2002), 1196-1212. [19] T. Li and H. Zhang, Information sharing in a supply chain with a make-to-stock manufacturer, Omega, 50 (2015), 115-125.  doi: 10.1016/j.omega.2014.08.001. [20] L. Li and H. Zhang, Confidentially and information sharing in supply chain coordination, Management Science, 54 (2008), 1467-1481. [21] B. K. Mishra, S. Raghunathan and X. Yue, Demand forecast sharing in supply chains, Production and Operations Management, 18 (2009), 152-166.  doi: 10.1111/j.1937-5956.2009.01013.x. [22] M. Raith, A general model of information in oligopoly, Journal of Economic Theory, 71 (1996), 260-288. [23] N. Shamir and H. Shin, Public forecast information sharing in a market with competing supply chains, Management Science, 62 (2016), 2994-3022. [24] W. Shang, A. Y. Ha and S. Tong, Information sharing in a supply chain with a common retailer, Management Science, 62 (2016), 245-263.  doi: 10.1287/mnsc.2014.2127. [25] N. Shi, S. Zhou, F. Wang, S. Xu and S. Xiong, Horizontal cooperation and information sharing between suppliers in the manufacturer-supplier triad, International Journal of Production Research, 52 (2014), 4526-4547.  doi: 10.1080/00207543.2013.869630. [26] M. Shnaiderman and F. El Ouardighi, The impact of partial information sharing in a two-echelon supply chain, Operations Research Letters, 42 (2014), 234-237.  doi: 10.1016/j.orl.2014.03.006. [27] P. D. Tai, T. T. H. Duc and J. Buddhakulsomsiri, Value of information sharing in supply chain under promotional competition, International Transactions in Operational Research, (2020), 1–33. doi: 10.1111/itor.12859. [28] X. Vives, Duopoly information equilibrium: Cournot and Bertrand, Journal of Economic Theory, 34 (1984), 71-94.  doi: 10.1016/0022-0531(84)90162-5. [29] J. Wei, J. Zhao and X. Hou, Bilateral information sharing in two supply chains with complementary products, Applied Mathematical Modelling, 72 (2019), 28-49.  doi: 10.1016/j.apm.2019.03.015. [30] R. Yan and Z. Pei, Incentive information sharing in various market structures, Decision Support Systems, 76 (2015), 76-86.  doi: 10.1016/j.dss.2015.03.003. [31] X. Yue and J. Liu, Demand forecast sharing in a dual-channel supply chain, European Journal of Operational Research, 174 (2006), 646-667.  doi: 10.1016/j.ejor.2004.12.020. [32] H. Zhang, Vertical information exchange in a supply chain with duopoly retailers, Production and Operations Management, 11 (2002), 531-546.  doi: 10.1111/j.1937-5956.2002.tb00476.x. [33] T. Zhang, X. Zhu, C. Zhou and M. Liu, Pricing and advertising the relief goods under various information sharing scenarios, International Transactions in Operational Research, 24 (2017), 867-889.  doi: 10.1111/itor.12221. [34] J. Zhao, W. Tang, R. Zhao and J. Wei, Pricing decisions for substitutable products with a common retailer in fuzzy environments, European Journal of Operational Research, 216 (2012), 409-419.  doi: 10.1016/j.ejor.2011.07.026. [35] X. Zhao, L. Xue and F. Zhang, Outsourcing competition and information sharing with asymmetrically informed suppliers, Production and Operations Management, 23 (2014), 1706-1718. [36] M. Zhou, B. Dan, S. Ma and X. Zhang, Supply chain coordination with information sharing: The informational advantage of GPOs, European Journal of Operational Research, 256 (2017), 785-802.  doi: 10.1016/j.ejor.2016.06.045.
Three information sharing patterns
Feasible region of information sharing
The effect of $\tau$ on the expected profits
The effect of $t$ on the expected profits
The effect of $\sigma$ on the expected profits
The effect of $\gamma$ on the expected profits
Notations and Descriptions
 Notation Descriptions $p_i$ retail price of product $i$, decided by retailer $w_i$ wholesale price of product $i$, decided by manufacturer $i$ $d_i$ demand of product $i$ $a$ determined market base $\varepsilon$ market demand uncertainty, a random variable with mean zero and variance $\sigma^2$ $\gamma$ competition between both manufacturers, which denotes the substitutability degree between products 1 and 2 $Y$ retailer's private demand information $y$ informed manufacturer's demand signal $t$ retailer's signal precision $\tau$ the amount of shared information $\pi_{m_i}$ profit of manufacturer $i$ $\pi_r$ profit of retailer $i$ $\Pi_{m_i}$ expected profit of manufacturer $i$ $\Pi_r$ expected profit of retailer $v_{m_i}$ value of manufacturer $i's$ information sharing $v_r$ value of retailer information sharing $V_{m_i}$ expected value of manufacturer $i's$ information sharing $V_r$ expected value of retailer information sharing
 Notation Descriptions $p_i$ retail price of product $i$, decided by retailer $w_i$ wholesale price of product $i$, decided by manufacturer $i$ $d_i$ demand of product $i$ $a$ determined market base $\varepsilon$ market demand uncertainty, a random variable with mean zero and variance $\sigma^2$ $\gamma$ competition between both manufacturers, which denotes the substitutability degree between products 1 and 2 $Y$ retailer's private demand information $y$ informed manufacturer's demand signal $t$ retailer's signal precision $\tau$ the amount of shared information $\pi_{m_i}$ profit of manufacturer $i$ $\pi_r$ profit of retailer $i$ $\Pi_{m_i}$ expected profit of manufacturer $i$ $\Pi_r$ expected profit of retailer $v_{m_i}$ value of manufacturer $i's$ information sharing $v_r$ value of retailer information sharing $V_{m_i}$ expected value of manufacturer $i's$ information sharing $V_r$ expected value of retailer information sharing
The maximal profits and the expected profits
 $X_iX_j=II$ $X_iX_j=IN$ $X_iX_j=NN$ The maximal $\pi^{II*}_{m_i}=\Phi_m+v^{II}_{m_i}$ $\pi^{IN*}_{m_i}=\Phi_m+v^{IN}_{m_i}$ $\pi^{NN*}_{m_i}=\Phi_m$ profits $\pi^{II*}_{m_j}=\Phi_m+v^{II}_{m_j}$ $\pi^{NI*}_{m_j}=\Phi_m+v^{NI}_{m_j}$ $\pi^{NN*}_{m_j}=\Phi_m$ $\pi^{II*}_r=\Phi_r+v^{II}_r$ $\pi^{IN*}_r=\Phi_r+v^{IN}_r$ $\pi^{NN*}_r=\Phi_r$ The expected $\Pi^{II*}_{m_i}=\overline{\Pi}_{m_i}+V^{II}_{m_i}$ $\Pi^{IN*}_{m_i} =\overline{\Pi}_{m_i}+V^{IN}_{m_i}$ $\Pi^{NN*}_{m_i}=\overline{\Pi}_{m_i}$ profits $\Pi^{II*}_{m_j}=\overline{\Pi}_{m_j}+V^{II}_{m_j}$ $\Pi^{NI*}_{m_j}=\overline\Pi_{m_j}$ $\Pi^{NN*}_{m_j}=\overline{\Pi}_{m_j}$ $\Pi^{II*}_r=\overline{\Pi}_r+F_r+V^{II}_r$ $\Pi^{IN*}_r=\overline{\Pi}_r+F_r+V^{IN}_r$ $\Pi^{NN*}_r=\overline{\Pi}_r+F_r$
 $X_iX_j=II$ $X_iX_j=IN$ $X_iX_j=NN$ The maximal $\pi^{II*}_{m_i}=\Phi_m+v^{II}_{m_i}$ $\pi^{IN*}_{m_i}=\Phi_m+v^{IN}_{m_i}$ $\pi^{NN*}_{m_i}=\Phi_m$ profits $\pi^{II*}_{m_j}=\Phi_m+v^{II}_{m_j}$ $\pi^{NI*}_{m_j}=\Phi_m+v^{NI}_{m_j}$ $\pi^{NN*}_{m_j}=\Phi_m$ $\pi^{II*}_r=\Phi_r+v^{II}_r$ $\pi^{IN*}_r=\Phi_r+v^{IN}_r$ $\pi^{NN*}_r=\Phi_r$ The expected $\Pi^{II*}_{m_i}=\overline{\Pi}_{m_i}+V^{II}_{m_i}$ $\Pi^{IN*}_{m_i} =\overline{\Pi}_{m_i}+V^{IN}_{m_i}$ $\Pi^{NN*}_{m_i}=\overline{\Pi}_{m_i}$ profits $\Pi^{II*}_{m_j}=\overline{\Pi}_{m_j}+V^{II}_{m_j}$ $\Pi^{NI*}_{m_j}=\overline\Pi_{m_j}$ $\Pi^{NN*}_{m_j}=\overline{\Pi}_{m_j}$ $\Pi^{II*}_r=\overline{\Pi}_r+F_r+V^{II}_r$ $\Pi^{IN*}_r=\overline{\Pi}_r+F_r+V^{IN}_r$ $\Pi^{NN*}_r=\overline{\Pi}_r+F_r$
Comparison on the effects of information sharing
 paper SC structure information effects of IS M R M R SC Zhang[32] 1-2 $\times$ $\surd$ B H BC Li [18] 1-n $\times$ $\surd$ B H BC Mishra et al. [21] 1-1 $\surd$ $\surd$ $\ast$ B H H $\star$ B H BC This paper 2-1 $\times$ $\surd$ $\ddagger$ B H H $\dagger$ B/N H H Note: M: manufacturer R: retailer SC: supply chain IS: information sharing B: beneficial H: harmful BC: beneficial under some conditions N: no effect $\ast$: make-to order scenario $\star$: make-to-stock scenario $\ddagger$: share with both manufacturers $\dagger$: share with one of manufacturers B/N: information sharing benefits the informed manufacturer, and has no effect on the uninformed manufacturer
 paper SC structure information effects of IS M R M R SC Zhang[32] 1-2 $\times$ $\surd$ B H BC Li [18] 1-n $\times$ $\surd$ B H BC Mishra et al. [21] 1-1 $\surd$ $\surd$ $\ast$ B H H $\star$ B H BC This paper 2-1 $\times$ $\surd$ $\ddagger$ B H H $\dagger$ B/N H H Note: M: manufacturer R: retailer SC: supply chain IS: information sharing B: beneficial H: harmful BC: beneficial under some conditions N: no effect $\ast$: make-to order scenario $\star$: make-to-stock scenario $\ddagger$: share with both manufacturers $\dagger$: share with one of manufacturers B/N: information sharing benefits the informed manufacturer, and has no effect on the uninformed manufacturer

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