The term probabilistic prize promotion refers to the activity of providing chances for consumers to win various kinds of prizes such as cash, gifts, opportunities to travel, and so on, through activities such as competition, prize drawing, or games (Kotler & Keller, 2006). Compared with other forms of promotion, probabilistic prize schemes are more flexible because they can fit into different structures with different content. However, many factors are likely to affect their effectiveness, such as prize structure, the value of promoted products, monetary value of the prizes, and the probability of winning a prize (Erev & Haruvy, 2010; Howard & Barry, 1990). When choosing probabilistic prize promotion as a marketing tool, promotion organizers tend to be subjective and blinkered (Erev & Haruvy, 2010). Therefore, a scientific, systematic, theoretical, and empirical study of the factors involved in the process of probabilistic prize promotion is likely to be of great practical value to those responsible for designing marketing strategies for enterprises.

Design is an important aspect in probabilistic prize promotion. However, in previous studies only probability levels under extreme conditions, that is, high or low probability, have been examined (e.g., Chen & Jia, 2005). Comparisons among various kinds of probabilities, including moderate levels and the intricate structure of incentive/probability design, have seldom been addressed in a real-life setting. In this study our aim was to determine the optimal design of incentives, first through a process of modeling, verification, and development, and then by experimenting with the propositions we had developed in the modeling stage and that were also based on relevant theories of behavioral economics.

Literature Review

Probability/prize design is the core of the study of probabilistic prize promotion schemes. Chen (2007) conducted research on the effectiveness of two different kinds of promotions, namely a low probability of winning a prize worth a large amount of money and a certainty of winning a gift of small monetary value. She found that when the promotion involves high-priced products, the former prize option proves more effective, whereas there is no significant difference between the two options when selling low-priced products.

Lin, Ke, and Tao (2008) found that, for high-priced products, as the prize value increases, the effect of the promotion takes the shape of a reversed U curve, and as the value declines, the effect takes the shape of a U curve. For low-priced products, the effect of the promotion was not found to be significantly different whether the prize was of a high or low value.

Some other scholars consider a probabilistic prize as an imprecise discount and have compared this with traditional sales promotions in which a discount is a fixed amount. They have found that, given the same promotion budget by the organizer of the promotion, a low probability of winning a high-value prize may lead to a greater number of sales (purchase intention) and thus higher profits, while a high probability of winning low-value prizes may not be as effective as traditional sales promotion measures (Dhar, González-Vallejo, & Soman, 1995). Scholars have also investigated the influence of factors such as the fit between a product and its giveaways, environment variables (e.g., store layout, ambience, and salience of promotion), consumer characteristics, and psychological factors such as self-perception, mental account, and emotion (Campbell & Diamond, 1990; Chandon, Wansink, & Laurent, 2000; Simonson, 1994; Song & Parry, 2009).

In general, the focus in previous studies on probabilistic prize promotion has been primarily on an extreme probability of winning, and a comparison of various probabilities, and complex real-life schemes have seldom been considered. Quiggin (1991) developed a model based on rank-dependent expected utility (RDEU) to examine general incentive schemes for a lottery.

Theoretical Modeling and Hypotheses

Research Based on Rank-dependent Expected Utility

We adopted the RDEU framework outlined by Quiggin (1991) to fit the context of a probabilistic prize promotion. In the RDEU model, the preference order “>” could be determined by the real-valued function V, which is further defined by the utility function U and the emotional function h. Mathematically, for the random variables X and Y, X > Y if and only if V(X,U,H) > V(Y,U,h).

Possible outcome (incentive) is represented by θ, which is ordered from worst to best, that is, θ ₁ ≤ θ ₂ ≤…≤ θ _N . θ possesses the property of discrete distribution: {θ , p} = {(θ ₁ ,θ ₂ ,..., θ _N); (p ₁ , p₂ ,..., p_N )}in which p_i is the correspondent probability of θ _i and



The weighting function q (q : [0,1] → [0,1]) is continuous and monotonically increasing such that q (0) = 0, q (1) = 1. According to the shapes of its curves, q(p) can be regarded as a pessimistic or optimistic reflection of probability p, which, as a result, can be used to describe decision makers’ psychological characteristics and emotions. RDEU is thus described as follows:



where



According to the RDEU model it is assumed that the utility function U (θ) is convex, which means risk averse, and that overweighting of small probabilities exists. q (p)/p is bounded and q ’( p ) is U-shaped.

The relationship between q (p) and p is illustrated in Figure 1.

Application of the Rank-dependent Expected Utility Model

Quiggin (1991) applied the RDEU model to the research of lotteries. By using the lottery system, the user tries to offer an optimal incentive structure based on lucky draws, thus offering a certain number of small and large prizes. In reality, the incentive structure of a probabilistic prize promotion has a similarly intricate structure. In our study we not only extended the research of Quiggin (1991), but incorporated the probabilistic prize promotion.

The following propositions were derived from this model:
P1: In terms of small prizes in a promotion with multi layer prize design, with a fixed budget, a selection of equal-value prizes at a certain probability is preferred to a series of different-value prizes at varied probabilities.
P2: In terms of large prize design, the preferred scheme is one in which there are a number of prizes with only one prize in each value category.
P3: For the single-layer structure, that is, all prizes with equal value, the preferred scheme is one in which there is a large prize with a small probability.
Regarding more complex structures, we tested a set of hypotheses.
H1: In a probabilistic prize promotion with a set budget, compared with a promotion in which one type of prize of low monetary value is offered, consumers will tend to prefer a variety of low-value prizes all of the same value plus a certain number of prizes of high monetary value.
H2: In probabilistic prize promotions, with the same budget and the same high-value prizes on offer, consumers will be inclined to favor a variety of prizes of the same low monetary value compared with a number of small prizes of different monetary values.
H3: In probabilistic prize promotions, with the same budget and the same small prizes, consumers’ will be more favorably disposed toward a sequence of prizes of increasingly high monetary value compared with a certain number of high-value prizes of equal monetary worth.
H4: In a single-layer structure, given the same budget, consumers will prefer to be offered only high-value prizes with a low probability of winning compared with only low-value prizes with a high probability of winning.

Chen and Jia (2005) found that overweighting of low probability is context dependent. The weighting of probabilities is affected by the differences among alternatives, decision makers’ wealth status, and other factors. However, it has been shown in empirical studies that the approach (giveaway or lucky draw) consumers prefer in promotion activities depends on the value of the promoted products (Chen & Jia, 2005; Chen, 2007). Accordingly, in this study, we also explored whether or not the value of the promoted products had an impact on our hypotheses being supported or not supported.

Method

Design and Participants

We conducted a 2 (promotion scheme: low-value prizes vs. low- plus high-value prizes) × 2 (product: bread vs. cell phone) mixed experiment to test the hypotheses. Both products in this study, namely the low-priced breads and the high-priced cell phones, are frequently purchased or used by, and very familiar to, consumers. Moreover, because many food companies and cell phone manufacturers choose probabilistic prize schemes to promote their products, this made our study quite close to reality. A promotional scheme was manipulated between subjects, and each participant was asked to answer questions about the two products. Graduate students (N = 63) at a university in northern China took part in the experiment in return for partial course credit, and all of them had previous bread and cell phone purchasing experiences.

Procedure

Participants were assigned randomly to one of the two conditions. After reading each scenario about either product, participants were asked to answer three sets of questions.

In the first set, they were asked to rate the promotion attractiveness, satisfaction with the promotion, and their purchase intention on a 5-point Likert scale (1 = very unlikely to buy; 5 = very likely to buy), as used in previous studies (Chandon et al., 2000; Inman & Zeelenberg, 2002). In the second set, they were presented with several pairs of schemes and asked to rate their degree of preference between the two schemes in each pair. The comparison was also measured on a 5-point scale (1 = scheme 1 is much better than scheme 2; 5 = scheme 2 is much better than scheme 1). Using the bread condition as an example, the schemes were designed as shown in Table 1.

The questionnaires also included an exploration of consumer reaction to moderately valuable prizes, which are frequently on offer in real life but have seldom been included in theoretical studies. For example, prizes between θ_k and θ_a are not included in the RDEU model. Therefore, in our study, in the third set, participants were asked to rank their preference for three alternative schemes: one offering a high-value prize plus many small prizes of equal value, one high-value prize plus some prizes of moderate value, and several equal high-value prizes. For the low-value bread condition, the three schemes were as follows: one prize worth RMB10,000 (equals approximately US$1,577) and 5,000 prizes worth RMB2 (US$0.32), one prize worth RMB10,000 and 50 prizes worth RMB200 (US$32), and 2 prizes worth RMB10,000, respectively. For the high-value cell phone condition, the three schemes each had one prize worth RMB30,000 (US$4,731) and 500 prizes worth RMB60 (US$9), one prize worth RMB30,000 and 50 prizes worth RMB600 (US$95), and 2 prizes worth RMB30,000, respectively. For both products, Scheme B provided prizes of moderate value.

Set 2 and Set 3 questions were identical for both groups of participants. Regarding the accessibility of the prizes, we used cash throughout our empirical study.

Materials

The scenario in the small prizes promotion /bread condition read as follows (translated from the original Chinese):
Suppose that a bread merchant is conducting a promotion with prizes awarded in the supermarket in your neighborhood. During a one-month promotional period starting from now, each purchaser of a bread item (priced at RMB10) will get a scratch card, with which he or she can find out the result and redeem the prize on the spot. It is claimed that a total of 10,000 prizes each valued at RMB2 will be guaranteed.

In the small plus big prizes condition, the last sentence was replaced by “It is claimed that one big prize valued at RMB10,000 and 5,000 prizes each valued at RMB2 will be guaranteed.”

The scenario in the small prizes promotion /cell phone condition read as follows:
Suppose that a mobile phone manufacturer is conducting a promotion with prizes awarded in the shopping mall in your neighborhood. During a one-month promotional period starting from now, each purchaser of a cell phone (priced at RMB1,500) will get a scratch card, with which he or she can find out the result and redeem the prize on the spot. It is claimed that a total of 1,000 prizes each valued at RMB60 will be guaranteed.

In the small plus big prizes condition, the last sentence was replaced by “It is claimed that one big prize valued at RMB30,000 and 500 prizes each valued at RMB60 will be guaranteed”.

Results

Data Analysis

All multiple item measures including purchase intention and satisfaction in the promotion reached acceptable reliability, that is, 0.70 and 0.72, respectively.

To test H1, that is, a variety of small prizes of equal value plus a number of large prizes would be preferred to a single layer of small prizes (Model 1), we conducted analyses of variance (ANOVA) among the two groups for each product. According to the results shown in Table 1 H1 was supported.

From the result of the paired samples t test of question No. 2 of set 2 we confirmed our hypothesis that consumers prefer a set of small prizes of equal value plus a number of large prizes (see Table 1). The results also show that, regardless of the product value, a set of small prizes of equal value plus a number of large prizes was preferred by participants in our study. Thus, we concluded that H1 was tenable.

We tested our other hypotheses via the other questions in set 2. With regard to H2, the average ratings for question 3 were 3.57 for bread and 3.29 for cell phones, which were both significantly higher than the indifference rating of 3, which indicated that our H2 was not supported, and that a number of large prizes in an increasingly valuable sequence, was preferred to a number of large prizes of the same value. With regard to H3, the average ratings for question 4 were 3.16 for bread and 3.13 for cell phones, both of which are higher than the indifference rating of 3 at the 1% significance level, thereby supporting H3. Again, this result suggests that a number of large prizes in an increasingly valuable sequence was preferred by our participants to a number of large prizes of the same value. H4 posits that offering just a set of small prizes with a high probability of winning is less desirable than offering just a set of large prizes with a low probability, of winning. We tested this proposition with question 1 and the average ratings were 2.54 for bread and 3.17 for cell phones. We were interested that the result for the cell phone group supported H4, but the result for the bread group did not support H4; we therefore concluded that product value matters. The findings provide incremental evidence for the contingent weighting model and consumer preference reversal (Nowlis & Simonson, 1997; Tversky, Sattath, & Slovic, 1988). The results are shown in Table 2.

Our findings are consistent with the results from previous similar studies on the comparison between a certain gain and winning a large amount when there is a low probability of doing so, which leads to the premise that overweighting of low probabilities is context dependent (Chen & Jia, 2005; Levy, 1997; McFadden, 1999). The theoretical analysis on the basis of RDEU that we used in this study is based on overweighting of low probabilities. This could account for the discordance between the theoretical result and the empirical analysis.

The hypotheses derived from the propositions do not address the comparison between large prizes at low probability and a large prize plus some small prizes at high probabilities. We explored this issue in question 5 of set 2. The results showed strong support in the preference of our participants for the latter option of both low- and high-value products.

In summary, a series of comparisons reveal a preference among probabilistic promotion schemes. Although the provision of only small prizes might sometimes be preferred to large prizes when the probability of winning is low, for example, in the case of low-value purchases, the addition of some prizes of high monetary value (keeping the budget unchanged) would always increase the attractiveness of the scheme.

By analyzing the ranking in set 3, we found that plan B, with moderately valuable prizes offered, gained the highest approval from consumers. The comparison based on bread shows that up to 52.38% of the consumers in our study selected plan B as their first choice; the percentage reaches as high as 61.90% when the comparison of their choice of plan was based on cell phones. Few consumers made plan B their third choice. Conversely, plan C was the third choice for most of them, and plan A remained a compromise between the two. A compromise effect – as suggested by Simonson (1989) in putting forward a theoretical justification for consumers’ purchase behavior from psychological and emotional perspectives – could contribute to this preference because our plan B represented a compromise choice.

Discussion

We investigated the configuration of schemes we had identified as optimal for probabilistic prize promotions. We found that high-value prizes are preferred when each of these represents an ascending order of increasing monetary value, and that promotions in which high-value prizes plus some prizes with a low monetary value are offered are always preferred to promotions in which only high- or low-value prizes are offered. In addition, we proved that REDU fits the situation of probabilistic prize promotion well.

The findings in our study contribute to existing knowledge about the effectiveness of probabilistic prize promotions. To our knowledge, no other scholars have empirically tested the complex structure of probability prize promotion design. The findings also have implications for promotion practices. When marketers design a probabilistic prize promotion scheme they should focus more on promotions in which both high- and low-value prizes are offered in preference to promotions in which only high- or low-value prizes are on offer. There are several limitations to our study. Firstly, in the real market, consumer behaviors are subject to a number of factors besides those that we examined in our study, such as environmental variables, consumer characteristics, and consumer psychology (Ward & Hill, 1991). In future studies researchers could explore the functioning mechanism of these factors and probe the possible interaction between them and probabilities and incentives by including other theoretical models, such as the prospect theory (Kahneman & Tversky, 1979) and including more variables such as the value of promoted products and wealth level of consumers.

Secondly, in assessing the effect of probabilistic prize promotions, apart from ranking of the prize value levels, factors that are of significance may include the range of prize levels, the difference between these different values, and how many of the prizes offered have the same value. Relevant theories, for example, the adaptation level theory, the interval theory, and the interval frequency theory, have been applied to many fields such as reference price (Briesch, Krishnamurthi, Mazumdar, & Raj, 1997; Janiszewski & Lichtenstein, 1999; Mazumdar, Raj, & Sinha, 2005; Thomas & Menon, 2007). Researchers in future studies could compare these models in terms of their explanatory effect of the effectiveness of probabilistic prize promotions.

Finally, because the participants in our study were all university students and our sample size was relatively small, in order that the conclusions in our research will have more theoretical generality, future researchers should extend the scope of their studies to other populations with a more comprehensive and larger sample.

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This research is supported by the National Natural Science Foundation of China (Grant No. 70802007

70872057

71172011

and 71172015) and MOE (Ministry of Education in China) Youth Project of Humanities and Social Sciences (Grant No. 11YJC630183).

Song Su, Department of Marketing, School of Economics and Business Administration, Beijing Normal University, Beijing, People’s Republic of China 100875. Email: [email protected]