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doi: 10.3934/jimo.2021167
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## Equity-based incentive to coordinate shareholder-manager interests under information asymmetry

 1 School of Management, Hefei University of Technology, Hefei 230009, China 2 Key Laboratory of Process Optimization and Intelligent Decision-Making of Ministry of Education, Hefei 230009, China 3 Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA 4 LANTA, High School of Economics, Moscow, Russia

*Corresponding author: Zhiping Zhou

Received  January 2021 Revised  July 2021 Early access September 2021

Fund Project: This research is supported by National Natural Science Foundation of China (Grant No. 72101077), and Anhui Provincial Natural Science Foundation (Grant No. 2008085QG341)

The shareholder's interest oriented from business operation relies on opportunism regulation of the manager under asymmetry. Effective motivation incentives should be exploited to facilitate the manager's effort devotion enthusiasms. This paper establishes a theoretic model in which the shareholder offers equity-based incentive to a fairness-preferred manager to coordinate their interest conflicts and maximize her expected revenue. The manager exerts unverifiable levels of efforts toward both decision and coordination tasks making the most of his private information about fairness preference. Two interrelated performance measures on different hierarchical levels are considered for contracting purposes. In each situation, we derive the equilibrium effort choices and incentive coefficients of both participants, and investigate how these decisions are affected by fairness preference. Research findings suggest that the incorporation of firm equity dominates pure profit incentive in eliciting high effort levels toward two distinctive managerial tasks. Besides, the equity-based incentive weakens the perceived unfairness and facilitates the participants' expected revenue. Comparative statics and numerical analysis are conducted to demonstrate our results and the effectiveness of the proposed equity-based incentive. Finally, we summarize the contributions of this paper and put forward directions for further study.

Citation: Zhiping Zhou, Yao Yin, Mi Zhou, Hao Cheng, Panos M. Pardalos. Equity-based incentive to coordinate shareholder-manager interests under information asymmetry. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2021167
##### References:
 [1] H. Ashbaugh-Skaife, D. W. Collins, W. R. Kinney and R. LaFond, The effect of SOX internal control deficiencies and their remediation on accrual quality, The Accounting Review, 83 (2008), 217-250.  doi: 10.2308/accr.2008.83.1.217. [2] F. Ballestín and R. Leus, Resource-constrained project scheduling for timely project completion with stochastic activity durations, Production and Operations Management, 18 (2009), 459-474.  doi: 10.1111/j.1937-5956.2009.01023.x. [3] F. Balmaceda, Optimal task assignments with loss-averse agents, European Economic Review, 105 (2018), 1-26.  doi: 10.1016/j.euroecorev.2018.03.006. [4] R. Bergmann and G. Friedl, Controlling innovative projects with moral hazard and asymmetric information, Research Policy, 37 (2008), 1504-1514.  doi: 10.1016/j.respol.2008.05.004. [5] F. Bova and L. Yang, Employee bargaining power, inter-firm competition, and equity-based compensation, Journal of Financial Economics, 126 (2017), 342-363.  doi: 10.1016/j.jfineco.2017.07.006. [6] S. Cato, The first-order approach to the principal-agent problems under inequality aversion, Operations Research Letters, 41 (2013), 526-529.  doi: 10.1016/j.orl.2013.06.012. [7] A. Chandrasekaran, K. Linderman and R. Schroeder, The role of project and organizational context in managing high-tech R & D projects, Production and Operations Management, 24 (2014), 560-586.  doi: 10.1111/poms.12253. [8] Z. Chen, Y. Lan and R. Zhao, Impacts of risk attitude and outside option on compensation contracts under different information structures, Fuzzy Optimization and Decision Making, 17 (2018), 13-47.  doi: 10.1007/s10700-016-9263-7. [9] W. Chi, T. X. Liu, X. Qian and Q. Ye, An experimental study of incentive contracts for short- and long-term employees, Journal of Economic Behavior and Organization, 159 (2019), 366-383.  doi: 10.1016/j.jebo.2019.02.006. [10] B. Corgnet, J. Gómez-Miñambres and R. Hernán-González, Goal setting in the principal-agent model: Weak incentives for strong performance, Games and Economic Behavior, 109 (2018), 311-326.  doi: 10.1016/j.geb.2017.12.017. [11] T. Dai, Z. Li and D. Sun, Equity-based incentives and supply chain buy-back contracts, Decision Sciences, 43 (2012), 661-685.  doi: 10.1111/j.1540-5915.2012.00363.x. [12] C. Ding, K. Wang and S. Lai, Channel coordination mechanism with retailers having fairness preference-An improved quantity discount mechanism, Journal of Industrial and Management Optimization, 9 (2013), 967-982.  doi: 10.3934/jimo.2013.9.967. [13] A. El-Tannir, Optimal project deadlines for mean-variance incentive contract designs, Computers & Industrial Engineering, 137 (2019), 106018.  doi: 10.1016/j.cie.2019.106018. [14] F. Englmaier and A. Wambach, Optimal incentive contracts under inequity aversion, Games and Economic Behavior, 69 (2010), 312-328.  doi: 10.1016/j.geb.2009.12.007. [15] H. Fu, M. Liu and B. Chen, Supplier's investment in manufacturers's quality improvement with equity holding, Journal of Industrial and Management Optimization, 17 (2021), 649-668.  doi: 10.3934/jimo.2019127. [16] J. Fu, X. Chen and Q. Hu, Subsidizing strategies in a sustainable supply chain, Journal of the Operational Research Society, 69 (2017), 283-295.  doi: 10.1057/s41274-017-0199-2. [17] H. Gan and M. S. Park, Are more able CEOs getting more compensated? Evidence from the pay-for-performance sensitivity of equity-based incentives, Advances in Accounting, 34 (2016), 64-76.  doi: 10.1016/j.adiac.2016.07.008. [18] H. Gao, Optimal compensation contracts when managers can hedge, Journal of Financial Economics, 97 (2010), 218-238.  doi: 10.1016/j.jfineco.2010.03.015. [19] X.-N. Gao and J. Tian, Multi-period incentive contract design in the agent emergency supplies reservation strategy with asymmetric information, Computers & Industrial Engineering, 120 (2018), 94-102.  doi: 10.1016/j.cie.2018.04.030. [20] J. Han and A. Rapoport, Intention-based fairness preferences in multi-partner project teams, Journal of Behavioral and Experimental Economics, 81 (2019), 84-90.  doi: 10.1016/j.socec.2019.06.003. [21] M. Hoffmann and M. Kolmar, Intention-based fairness preferences in two-player contests, Economics Letters, 120 (2013), 276-279.  doi: 10.1016/j.econlet.2013.04.038. [22] A. Intezari and D. J. Pauleen, Conceptualizing wise management decision-making: A grounded theory approach, Decision Sciences, 49 (2018), 335-400.  doi: 10.1111/deci.12267. [23] J.-P. Kallunki, E. Pyykkö and T. Laamanen, Stock market valuation, profitability and R & D spending of the firm: The effect of technology mergers and acquisitions, Journal of Business Finance & Accounting, 36 (2009), 838-862.  doi: 10.1111/j.1468-5957.2009.02161.x. [24] E. Katok and V. Pavlov, Fairness in supply chain contracts: A laboratory study, Journal of Operations Management, 31 (2013), 129-137.  doi: 10.1016/j.jom.2013.01.001. [25] L. P. Kerkhove and M. Vanhoucke, Incentive contract design for projects: The owner's perspective, Omega, 62 (2016), 93-114.  doi: 10.1016/j.omega.2015.09.002. [26] Y. Khoroshilov and M. P. Narayanan, The role of profit-based and stock-based components in incentive compensation, Journal of Financial Intermediation, 17 (2008), 357-378.  doi: 10.1016/j.jfi.2008.02.005. [27] M. Kong, J. Pei, J. Xu, X. Liu, X. Yu and P. M. Pardalos, A robust optimization approach for integrated steel production and batch delivery scheduling with uncertain rolling times and deterioration effect, International Journal of Production Research, 58 (2020), 5132-5154.  doi: 10.1080/00207543.2019.1693659. [28] H. D. Kwon, S. A. Lippman and C. S. Tang, Optimal time-based and cost-based coordinated project contracts with unobservable work rates, International Journal of Production Economics, 126 (2010), 247-254.  doi: 10.1016/j.ijpe.2010.03.013. [29] H.-H. Lee and C. Li, Supplier quality management: Investment, inspection, and incentives, Production and Operations Management, 27 (2017), 304-322.  doi: 10.1111/poms.12802. [30] J. Liu, R. Gao, C. Y. J. Cheah and J. Luo, Incentive mechanism for inhibiting investors'opportunistic behavior in PPP projects, International Journal of Project Management, 34 (2016), 1102-1111.  doi: 10.1016/j.ijproman.2016.05.013. [31] T. Nohel and S. Todd, Compensation for managers with career concerns: The role of stock options in optimal contracts, Journal of Corporate Finance, 11 (2005), 229-251.  doi: 10.1016/S0929-1199(03)00047-6. [32] V. O'Connell, J.-H. Lee and D. O'Sullivan, The influence of CEO equity incentives on licensing, European Management Journal, 36 (2018), 266-277.  doi: 10.1016/j.emj.2018.01.005. [33] J. Oxley and G. Pandher, Equity-based incentives and collaboration in the modern multibusiness firm, Strategic Management Journal, 37 (2016), 1379-1394.  doi: 10.1002/smj.2392. [34] E. Siemsen, S. Balasubramanian and A. V. Roth, Incentives that induce task-related effort, helping, and knowledge sharing in workgroups, Management Science, 53 (2007), 1533-1550.  doi: 10.1287/mnsc.1070.0714. [35] N. Siggelkow, Misperceiving interactions among complements and substitutes: Organizational consequences, Management Science, 48 (2002), 900-916.  doi: 10.1287/mnsc.48.7.900.2820. [36] R. Silvers, The value of information in a principal-agent model with moral hazard: The ex ante contracting case, Games & Economic Behavior, 74 (2012), 352-365.  doi: 10.1016/j.geb.2011.07.002. [37] G. Strobl, Stock-based managerial compensation, price informativeness, and the incentive to overinvest, Journal of Corporate Finance, 29 (2014), 594-606.  doi: 10.1016/j.jcorpfin.2013.12.003. [38] M. Suprapto, H. L. M. Bakker, H. G. Mooi and M. J. C. M. Hertogh, Hertogh, How do contract types and incentives matter to project performance?, International Journal of Project Management, 34 (2015), 1071-1087.  doi: 10.1016/j.ijproman.2015.08.003. [39] X. Yan, H.-Y. Chong, J. Zhou, Z. Sheng and F. Xu, Fairness preference based decision-making model for concession period in PPP projects, Journal of Industrial and Management Optimization, 16 (2020), 11-23.  doi: 10.3934/jimo.2018137. [40] K. Yang, R. Zhao and Y. Lan, Impacts of uncertain project duration and asymmetric risk sensitivity information in project management, International Transactions in Operational Research, 23 (2016), 749-774.  doi: 10.1111/itor.12156. [41] C. Zhou, J. Peng, Z. Liu and B. Dong, Optimal incentive contracts under loss aversion and inequity aversion, Fuzzy Optimization and Decision Making, 18 (2019), 85-102.  doi: 10.1007/s10700-018-9288-1.

show all references

##### References:
 [1] H. Ashbaugh-Skaife, D. W. Collins, W. R. Kinney and R. LaFond, The effect of SOX internal control deficiencies and their remediation on accrual quality, The Accounting Review, 83 (2008), 217-250.  doi: 10.2308/accr.2008.83.1.217. [2] F. Ballestín and R. Leus, Resource-constrained project scheduling for timely project completion with stochastic activity durations, Production and Operations Management, 18 (2009), 459-474.  doi: 10.1111/j.1937-5956.2009.01023.x. [3] F. Balmaceda, Optimal task assignments with loss-averse agents, European Economic Review, 105 (2018), 1-26.  doi: 10.1016/j.euroecorev.2018.03.006. [4] R. Bergmann and G. Friedl, Controlling innovative projects with moral hazard and asymmetric information, Research Policy, 37 (2008), 1504-1514.  doi: 10.1016/j.respol.2008.05.004. [5] F. Bova and L. Yang, Employee bargaining power, inter-firm competition, and equity-based compensation, Journal of Financial Economics, 126 (2017), 342-363.  doi: 10.1016/j.jfineco.2017.07.006. [6] S. Cato, The first-order approach to the principal-agent problems under inequality aversion, Operations Research Letters, 41 (2013), 526-529.  doi: 10.1016/j.orl.2013.06.012. [7] A. Chandrasekaran, K. Linderman and R. Schroeder, The role of project and organizational context in managing high-tech R & D projects, Production and Operations Management, 24 (2014), 560-586.  doi: 10.1111/poms.12253. [8] Z. Chen, Y. Lan and R. Zhao, Impacts of risk attitude and outside option on compensation contracts under different information structures, Fuzzy Optimization and Decision Making, 17 (2018), 13-47.  doi: 10.1007/s10700-016-9263-7. [9] W. Chi, T. X. Liu, X. Qian and Q. Ye, An experimental study of incentive contracts for short- and long-term employees, Journal of Economic Behavior and Organization, 159 (2019), 366-383.  doi: 10.1016/j.jebo.2019.02.006. [10] B. Corgnet, J. Gómez-Miñambres and R. Hernán-González, Goal setting in the principal-agent model: Weak incentives for strong performance, Games and Economic Behavior, 109 (2018), 311-326.  doi: 10.1016/j.geb.2017.12.017. [11] T. Dai, Z. Li and D. Sun, Equity-based incentives and supply chain buy-back contracts, Decision Sciences, 43 (2012), 661-685.  doi: 10.1111/j.1540-5915.2012.00363.x. [12] C. Ding, K. Wang and S. Lai, Channel coordination mechanism with retailers having fairness preference-An improved quantity discount mechanism, Journal of Industrial and Management Optimization, 9 (2013), 967-982.  doi: 10.3934/jimo.2013.9.967. [13] A. El-Tannir, Optimal project deadlines for mean-variance incentive contract designs, Computers & Industrial Engineering, 137 (2019), 106018.  doi: 10.1016/j.cie.2019.106018. [14] F. Englmaier and A. Wambach, Optimal incentive contracts under inequity aversion, Games and Economic Behavior, 69 (2010), 312-328.  doi: 10.1016/j.geb.2009.12.007. [15] H. Fu, M. Liu and B. Chen, Supplier's investment in manufacturers's quality improvement with equity holding, Journal of Industrial and Management Optimization, 17 (2021), 649-668.  doi: 10.3934/jimo.2019127. [16] J. Fu, X. Chen and Q. Hu, Subsidizing strategies in a sustainable supply chain, Journal of the Operational Research Society, 69 (2017), 283-295.  doi: 10.1057/s41274-017-0199-2. [17] H. Gan and M. S. Park, Are more able CEOs getting more compensated? Evidence from the pay-for-performance sensitivity of equity-based incentives, Advances in Accounting, 34 (2016), 64-76.  doi: 10.1016/j.adiac.2016.07.008. [18] H. Gao, Optimal compensation contracts when managers can hedge, Journal of Financial Economics, 97 (2010), 218-238.  doi: 10.1016/j.jfineco.2010.03.015. [19] X.-N. Gao and J. Tian, Multi-period incentive contract design in the agent emergency supplies reservation strategy with asymmetric information, Computers & Industrial Engineering, 120 (2018), 94-102.  doi: 10.1016/j.cie.2018.04.030. [20] J. Han and A. Rapoport, Intention-based fairness preferences in multi-partner project teams, Journal of Behavioral and Experimental Economics, 81 (2019), 84-90.  doi: 10.1016/j.socec.2019.06.003. [21] M. Hoffmann and M. Kolmar, Intention-based fairness preferences in two-player contests, Economics Letters, 120 (2013), 276-279.  doi: 10.1016/j.econlet.2013.04.038. [22] A. Intezari and D. J. Pauleen, Conceptualizing wise management decision-making: A grounded theory approach, Decision Sciences, 49 (2018), 335-400.  doi: 10.1111/deci.12267. [23] J.-P. Kallunki, E. Pyykkö and T. Laamanen, Stock market valuation, profitability and R & D spending of the firm: The effect of technology mergers and acquisitions, Journal of Business Finance & Accounting, 36 (2009), 838-862.  doi: 10.1111/j.1468-5957.2009.02161.x. [24] E. Katok and V. Pavlov, Fairness in supply chain contracts: A laboratory study, Journal of Operations Management, 31 (2013), 129-137.  doi: 10.1016/j.jom.2013.01.001. [25] L. P. Kerkhove and M. Vanhoucke, Incentive contract design for projects: The owner's perspective, Omega, 62 (2016), 93-114.  doi: 10.1016/j.omega.2015.09.002. [26] Y. Khoroshilov and M. P. Narayanan, The role of profit-based and stock-based components in incentive compensation, Journal of Financial Intermediation, 17 (2008), 357-378.  doi: 10.1016/j.jfi.2008.02.005. [27] M. Kong, J. Pei, J. Xu, X. Liu, X. Yu and P. M. Pardalos, A robust optimization approach for integrated steel production and batch delivery scheduling with uncertain rolling times and deterioration effect, International Journal of Production Research, 58 (2020), 5132-5154.  doi: 10.1080/00207543.2019.1693659. [28] H. D. Kwon, S. A. Lippman and C. S. Tang, Optimal time-based and cost-based coordinated project contracts with unobservable work rates, International Journal of Production Economics, 126 (2010), 247-254.  doi: 10.1016/j.ijpe.2010.03.013. [29] H.-H. Lee and C. Li, Supplier quality management: Investment, inspection, and incentives, Production and Operations Management, 27 (2017), 304-322.  doi: 10.1111/poms.12802. [30] J. Liu, R. Gao, C. Y. J. Cheah and J. Luo, Incentive mechanism for inhibiting investors'opportunistic behavior in PPP projects, International Journal of Project Management, 34 (2016), 1102-1111.  doi: 10.1016/j.ijproman.2016.05.013. [31] T. Nohel and S. Todd, Compensation for managers with career concerns: The role of stock options in optimal contracts, Journal of Corporate Finance, 11 (2005), 229-251.  doi: 10.1016/S0929-1199(03)00047-6. [32] V. O'Connell, J.-H. Lee and D. O'Sullivan, The influence of CEO equity incentives on licensing, European Management Journal, 36 (2018), 266-277.  doi: 10.1016/j.emj.2018.01.005. [33] J. Oxley and G. Pandher, Equity-based incentives and collaboration in the modern multibusiness firm, Strategic Management Journal, 37 (2016), 1379-1394.  doi: 10.1002/smj.2392. [34] E. Siemsen, S. Balasubramanian and A. V. Roth, Incentives that induce task-related effort, helping, and knowledge sharing in workgroups, Management Science, 53 (2007), 1533-1550.  doi: 10.1287/mnsc.1070.0714. [35] N. Siggelkow, Misperceiving interactions among complements and substitutes: Organizational consequences, Management Science, 48 (2002), 900-916.  doi: 10.1287/mnsc.48.7.900.2820. [36] R. Silvers, The value of information in a principal-agent model with moral hazard: The ex ante contracting case, Games & Economic Behavior, 74 (2012), 352-365.  doi: 10.1016/j.geb.2011.07.002. [37] G. Strobl, Stock-based managerial compensation, price informativeness, and the incentive to overinvest, Journal of Corporate Finance, 29 (2014), 594-606.  doi: 10.1016/j.jcorpfin.2013.12.003. [38] M. Suprapto, H. L. M. Bakker, H. G. Mooi and M. J. C. M. Hertogh, Hertogh, How do contract types and incentives matter to project performance?, International Journal of Project Management, 34 (2015), 1071-1087.  doi: 10.1016/j.ijproman.2015.08.003. [39] X. Yan, H.-Y. Chong, J. Zhou, Z. Sheng and F. Xu, Fairness preference based decision-making model for concession period in PPP projects, Journal of Industrial and Management Optimization, 16 (2020), 11-23.  doi: 10.3934/jimo.2018137. [40] K. Yang, R. Zhao and Y. Lan, Impacts of uncertain project duration and asymmetric risk sensitivity information in project management, International Transactions in Operational Research, 23 (2016), 749-774.  doi: 10.1111/itor.12156. [41] C. Zhou, J. Peng, Z. Liu and B. Dong, Optimal incentive contracts under loss aversion and inequity aversion, Fuzzy Optimization and Decision Making, 18 (2019), 85-102.  doi: 10.1007/s10700-018-9288-1.
The sequence of events and actions
The impact of fairness preference on managerial effort levels
The impact of fairness preference on bonus coefficients
The impact of fairness preference on participants' benefits
The impacts of effort contributions and performance variances on shareholder's revenue
NOTATIONS AND PARAMETERS
 Symbol Meaning $a_d,a_c$ The managerial effort levels toward decision and coordination tasks, $a_d,a_c\ge 0$; $k(a_d,a_c)$ The manager's total effort cost, in which the parameter $\delta$ captures the task synergy effect; $p$ The firm's stochastic accounting profit with noise term ${\varepsilon _p} \sim N(0,\sigma_p^2)$; $\mu_d$ The contribution of manager's decision task effort on firm's accounting profit, $\mu_d >0$; $v$ The firm's stochastic stock value with noise term ${\varepsilon _v} \sim N(0,\sigma_v^2)$; $\mu_c,\lambda_p$ The contribution of coordination task effort and firm's accounting profit on its stock value respectively, $\mu_c >0,\lambda_p >0$; $\alpha_0,\alpha_p,\alpha_v$ The fixed compensation and incentive coefficients respectively, $\alpha_p,\alpha_v\in(0,1)$; $\beta,\hat\beta$ The manager's actual and reported fairness preference coefficients, $\beta,\hat\beta\in[0,\bar \beta]$; $\gamma$ The manager's comparative fair ratio between the participants'net incomes, $\gamma\in(0,1)$; $\rho$ The risk-averse coefficient of the manager, $\rho >0$; $\pi_m,\pi_s$ The net incomes of the manager and the shareholder respectively; $CE_m$ The manager's certainty equivalent based on his perceived utility $U_m$.
 Symbol Meaning $a_d,a_c$ The managerial effort levels toward decision and coordination tasks, $a_d,a_c\ge 0$; $k(a_d,a_c)$ The manager's total effort cost, in which the parameter $\delta$ captures the task synergy effect; $p$ The firm's stochastic accounting profit with noise term ${\varepsilon _p} \sim N(0,\sigma_p^2)$; $\mu_d$ The contribution of manager's decision task effort on firm's accounting profit, $\mu_d >0$; $v$ The firm's stochastic stock value with noise term ${\varepsilon _v} \sim N(0,\sigma_v^2)$; $\mu_c,\lambda_p$ The contribution of coordination task effort and firm's accounting profit on its stock value respectively, $\mu_c >0,\lambda_p >0$; $\alpha_0,\alpha_p,\alpha_v$ The fixed compensation and incentive coefficients respectively, $\alpha_p,\alpha_v\in(0,1)$; $\beta,\hat\beta$ The manager's actual and reported fairness preference coefficients, $\beta,\hat\beta\in[0,\bar \beta]$; $\gamma$ The manager's comparative fair ratio between the participants'net incomes, $\gamma\in(0,1)$; $\rho$ The risk-averse coefficient of the manager, $\rho >0$; $\pi_m,\pi_s$ The net incomes of the manager and the shareholder respectively; $CE_m$ The manager's certainty equivalent based on his perceived utility $U_m$.
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