# Consumer Value-Maximizing Sweepstakes & Contests: A Theoretical and Experimental Investigation

36 Pages Posted: 7 May 2002

Date Written: February 27, 2002

### Abstract

Sweepstakes and contests are an extremely common promotional strategy used by firms. The sweepstakes and contests often differ significantly in the design of reward structure. For example, in 1999, Godiva Chocolates conducted a sweepstakes where one box of chocolates contained a diamond jewellery. The chance of winning was 1 in 320,000. In 2000, M&M conducted a contest where the Grand Prize of a $1,000,000 had winning odds of 1 in 380,000,000 and a million second prizes of a coupon redeemable for a M&M packet had the odds of 1 in 380. In a contest conducted by Planters in 2000, the first prize too was a $1 m (odds 1 in 5,000,000) but there were only 100 second prizes of a NFL football jacket with odds of 1 in 50,000. In 1999, Old Navy conducted a sweepstake where there were 4,552 first prize winners who got $100 gift cards with the odds of winning 1 in 1,000, the 9,105 second prize of $ 20 gift certificates had odds of 1 in 500 and the 13,660 third prizes of $10 certificates and 883,476 fourth prizes of $5 had winning odds of 1 in 333 and 1 in 50 respectively. These examples raise the issue of how reward structure would affect consumer valuation and participation. The objective of this paper is to obtain an understanding of how consumers' valuation of sweepstakes varies on the basis of differing consumer segments and the characteristics of the consumers.

Our paper focuses on the decisions pertaining to the reward structure. We examine some commonly used sweepstakes and provide insights on how consumer valuations depend on the number of winners, the number of levels of prizes, and the difference in the awards between the levels (reward spread). We follow the Cumulative Prospect Theory to develop a model for consumer valuations of alternative formats of sweepstakes. The model applies a S-shaped probability weighting function and a loss-aversion framework for the consumers who switched to less preferred brands for sweepstakes but eventually did not win any prizes. We analytically derive our theoretical results and experimentally test some of the key implications.

The results of the model show that the sweepstakes reward structure should be based on three factors: the objectives of the firm, the risk aversion of the customers, and the level of sub-additivity of probability weighting. The results of the model prescribes that the firm should begin by setting sweepstake objectives in terms of either attracting switchers or targeting current users. If the objective is to target current users, then the number of prizes awarded should be lower than in the case where the targets are switchers. If the current users are risk neutral, then the consumer value-maximizing award is a single grand prize. If the current users are risk averse, then the award should consist of multiple "large" prizes. When the firm's objective is to draw sales away from competitors, the value-maximizing strategy is to distribute the award money over more prizes. If the non-current user segment is risk neutral with respect to gains but sufficiently risk averse in the domain of losses, then the prescribed reward structure is to have a single grand prize but also include several small prizes which ideally should be close to the opportunity cost of the customers. If the non-loyal customers are risk averse in gain and loss averse, then the best prize allocation is to have both multiple large prizes as well as several small prizes.

Another recommendation from the model analysis is that the firm should minimize the number of prizes at each level. In practice, the costs of implementing and communicating such a prize structure could be high. To trade-off between the logistical and communication costs and the theoretically value-maximizing approach, firms could increase the number of prizes at each level for easier implementation. A trade-off is involved between increasing the attractiveness of the sweepstake and the implementation costs of administering several levels of prizes. Often, when the prizes are products rather than cash, the firm may obtain quantity discounts for the products but the value of the products will be the same for the sweepstake participants.

**Keywords:** Sales promotion, prospect theory, customer loyalty

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