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Designing Optimal Sales Contests: A Theoretical Perspective

Author

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  • Ajay Kalra

    () (Graduate School of Industrial Administration, Carnegie Mellon University)

  • Mengze Shi

    () (Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

Abstract

Sales contests are commonly used by firms as a short-term motivational device to increase salespeople's efforts. Conceptually, sales contests and piece-rate schemes, such as salary, commission, or quotas, differ in that in sales contests payment to salespeople is based on relative rather than absolute sales levels. Using the agency theoretic framework where the firm is risk neutral and the salespeople are risk averse, we examine how a firm should design an optimal contest to maximize its profit through stimulating salespeople's efforts. Specifically, we investigate how many salespeople should be given awards and how the reward should be allocated between the winners. Three commonly used sales contest formats are studied. In the first format, termed as Rank-Order Tournament, there are many winners and the amount of reward is based on relative rank achieved, with larger amounts awarded to higher ranks. We also examine two special cases of Rank-Ordered Tournament: a Multiple-Winners format, where the reward is shared equally, and a Winner-Take-All format, where a single winner gets the entire reward. We model salespeople's behavior by considering utility of the reward from achieving one of the winning ranks in the contest and assessing incremental chances of winning by exerting more effort. The analysis was done for two situations based on whether the total reward is large enough for salespeople to participate in the effort-maximizing sales contest or not. The analysis shows that factors impacting contest design include the salespeople's degree of risk aversion, number of salespeople competing in the contest, and degree of sales uncertainty (which reflects strength of the sales-effort relationship). The results show that salespeople exert lower effort when there are larger numbers of participants or when sales uncertainty is high. We find that the Rank-Order Tournament is superior to the Multiple-Winners contest format. In a Multiple-Winners format, the salesperson whose performance is just sufficient to win is better off than any of the other winners as he exerts the least effort to win but obtains as high a reward as any other winners. Specific recommendations on contest designs are obtained assuming that sales follow either a logistic or uniform distribution. Assuming that sales outcome is logistically distributed and the contest budget is high enough to ensure participation, our analysis shows that the total number of winners in a sales contest should not exceed half the number of the contestants. This result is due to the symmetric nature of the logistic distribution. Our analysis also indicates that the total number of winners should be increased and the spread decreased when salespeople are more risk averse. When salespeople are more risk averse, their marginal values for higher rewards become smaller. The spread should increase with ranks when rate of risk tolerance is high and decrease with ranks when the rate of risk tolerance is lower. In the extreme case of risk-neutral salespeople, the optimal design is a Winner-Take-All format. We also conclude that since the probability of winning the contest decreases with number of contestants, the optimal number of winners should increase and interrank spread decrease when there are a larger number of participants. If the firm does not allocate a large enough budget for salespeople to participate in the effort-maximizing sales contest, then the firm may increase the number of winners to more than half the sales-force. Increasing the number of winners and decreasing the spread are required to encourage the salespeople to participate, particularly when there are many participants who are risk averse. A counterintuitive result is that the number of winners should be reduced and the spread increased when sales uncertainty is high. Increasing sales uncertainty leads to lower equilibrium effort levels while keeping the expected utility of the contest rewards the same. Therefore, increased uncertainty results in higher participation incentive. The firm should thus relatively reduce the number of winners in high-uncertainty situations. Under the assumption of uniformly distributed sales, the recommendation is that a Winner-Take-All contest induces maximum efforts regardless of the level of risk aversion, number of players, or the degree of uncertainty. When the Winner-Take-All format does not meet the participation constraint, our analysis recommends offering a big reward to the top salesperson and a small reward to many other sales-people. The small reward should be just sufficient to ensure that all salespeople participate. Consistent with logistic distribution, the spread should decrease when salespeople are more risk averse or there are more players but should increase when sales uncertainty is larger. These results highlight that some of the conclusions drawn may be sensitive to distributional assumptions.

Suggested Citation

  • Ajay Kalra & Mengze Shi, 2001. "Designing Optimal Sales Contests: A Theoretical Perspective," Marketing Science, INFORMS, vol. 20(2), pages 170-193, December.
  • Handle: RePEc:inm:ormksc:v:20:y:2001:i:2:p:170-193
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    File URL: http://dx.doi.org/10.1287/mksc.20.2.170.10193
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    References listed on IDEAS

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    Cited by:

    1. Emmanuel Dechenaux & Dan Kovenock & Roman Sheremeta, 2015. "A survey of experimental research on contests, all-pay auctions and tournaments," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 609-669, December.
    2. Verbeke, Willem & Bagozzi, Richard P. & Belschak, Frank D., 2016. "The role of status and leadership style in sales contests: A natural field experiment," Journal of Business Research, Elsevier, vol. 69(10), pages 4112-4120.
    3. Hua Chen & Sung H. Ham & Noah Lim, 2011. "Designing Multiperson Tournaments with Asymmetric Contestants: An Experimental Study," Management Science, INFORMS, vol. 57(5), pages 864-883, May.
    4. Ajay Kalra & Mengze Shi & Kannan Srinivasan, 2003. "Salesforce Compensation Scheme and Consumer Inferences," Management Science, INFORMS, vol. 49(5), pages 655-672, May.
    5. Nadarajah, Saralees & Kotz, Samuel, 2009. "Models for purchase frequency," European Journal of Operational Research, Elsevier, vol. 192(3), pages 1014-1026, February.
    6. Clark, Derek J. & Nilssen, Tore & Sand, Jan Yngve, 2012. "Motivating over Time: Dynamic Win Effects in Sequential Contests," Memorandum 28/2012, Oslo University, Department of Economics.
    7. Pavel Kireyev, 2016. "Markets for Ideas: Prize Structure, Entry Limits, and the Design of Ideation Contests," Harvard Business School Working Papers 16-129, Harvard Business School.
    8. Ramarao Desiraju, 2004. "Costs and Benefits of Inducing Intrabrand Competition: The Role of Limited Liability," Marketing Science, INFORMS, vol. 23(3), pages 429-450, March.
    9. Niladri Syam & James Hess & Ying Yang, 2013. "Sales contests versus quotas with imbalanced territories," Marketing Letters, Springer, vol. 24(3), pages 229-244, September.
    10. Budde, Jörg, 2009. "Information in tournaments under limited liability," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 59-72, January.
    11. Jed DeVaro & Antti Kauhanen, 2016. "An “Opposing Responses” Test of Classic versus Market-Based Promotion Tournaments," Journal of Labor Economics, University of Chicago Press, vol. 34(3), pages 747-779.
    12. Birendra K. Mishra & Ashutosh Prasad, 2004. "Centralized Pricing Versus Delegating Pricing to the Salesforce Under Information Asymmetry," Marketing Science, INFORMS, vol. 23(1), pages 21-27, January.
    13. Wilfred Amaldoss & Teck-Hua Ho & Aradhna Krishna & Kay-Yut Chen & Preyas Desai & Ganesh Iyer & Sanjay Jain & Noah Lim & John Morgan & Ryan Oprea & Joydeep Srivasatava, 2008. "Experiments on strategic choices and markets," Marketing Letters, Springer, vol. 19(3), pages 417-429, December.
    14. Kräkel, Matthias & Schöttner, Anja, 2010. "Technology choice, relative performance pay, and worker heterogeneity," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 748-758, December.
    15. Christian Terwiesch & Yi Xu, 2008. "Innovation Contests, Open Innovation, and Multiagent Problem Solving," Management Science, INFORMS, vol. 54(9), pages 1529-1543, September.
    16. Ying Yang & Niladri Syam & James Hess, 2013. "Thrill of victory and agony of defeat: Emotional rewards and sales force compensation," Quantitative Marketing and Economics (QME), Springer, vol. 11(4), pages 379-402, December.
    17. Ewerhart, Christian, 2016. "An envelope approach to tournament design," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 1-9.
    18. Murali Mantrala & Sönke Albers & Fabio Caldieraro & Ove Jensen & Kissan Joseph & Manfred Krafft & Chakravarthi Narasimhan & Srinath Gopalakrishna & Andris Zoltners & Rajiv Lal & Leonard Lodish, 2010. "Sales force modeling: State of the field and research agenda," Marketing Letters, Springer, vol. 21(3), pages 255-272, September.
    19. Pushkar Murthy & Murali Mantrala, 2005. "Allocating a Promotion Budget between Advertising and Sales Contest Prizes: An Integrated Marketing Communications Perspective," Marketing Letters, Springer, vol. 16(1), pages 19-35, January.
    20. Costin DAMASARU & Radu CAMENITA & Cristina ANDREESCU (MANOLACHE), 2011. "How Can We Increase Sales Force Motivation? Practical Approach: Stimulating Motivation on a Telecom Companies` Sales Force," REVISTA DE MANAGEMENT COMPARAT INTERNATIONAL/REVIEW OF INTERNATIONAL COMPARATIVE MANAGEMENT, Faculty of Management, Academy of Economic Studies, Bucharest, Romania, vol. 12(6), pages 261-267, December.
    21. James W. Bono, 2008. "Sales contests, promotion decisions and heterogeneous risk," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 29(4), pages 371-382.
    22. Saif Benjaafar & Ehsan Elahi & Karen L. Donohue, 2007. "Outsourcing via Service Competition," Management Science, INFORMS, vol. 53(2), pages 241-259, February.
    23. Yan Dong & Yuliang Yao & Tony Haitao Cui, 2011. "When Acquisition Spoils Retention: Direct Selling vs. Delegation Under CRM," Management Science, INFORMS, vol. 57(7), pages 1288-1299, July.
    24. Ladley, Daniel & Wilkinson, Ian & Young, Louise, 2015. "The impact of individual versus group rewards on work group performance and cooperation: A computational social science approach," Journal of Business Research, Elsevier, vol. 68(11), pages 2412-2425.
    25. Clark, Derek J. & Nilssen , Tore & Sand, Jan Yngve, 2014. "Keep on Fighting: Dynamic Win Effects in an All-Pay Auction," Memorandum 23/2014, Oslo University, Department of Economics.

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