Designing Optimal Sales Contests: A Theoretical Perspective

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...

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