Designing Optimal Sales Contests: A Theoretical Perspective
Authors: Kalra Ajay , Shi Mengze 
Published: December 2003

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.