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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.
http://portal.acm.org/citation.cfm?id=769267
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