When Retailing and Las Vegas Meet: Probabilistic Free...

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When Retailing and Las Vegas Meet: Probabilistic FreePrice PromotionsNina Mazar, Kristina Shampanier, Dan Ariely

To cite this article:Nina Mazar, Kristina Shampanier, Dan Ariely (2016) When Retailing and Las Vegas Meet: Probabilistic Free Price Promotions.Management Science

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When Retailing and Las Vegas Meet:Probabilistic Free Price Promotions

Nina MazarRotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada, [email protected]

Kristina ShampanierAnalysis Group, Boston, Massachusetts 02199, [email protected]

Dan ArielyDuke University, Durham, North Carolina 27705, [email protected]

A number of retailers offer gambling- or lottery-type price promotions with a chance to receive one’s entirepurchase for free. Although these retailers seem to share the intuition that probabilistic free price promo-

tions are attractive to consumers, it is unclear how they compare to traditional sure price promotions of equalexpected monetary value. We compared these two risky and sure price promotions for planned purchases acrosssix experiments in the field and in the laboratory. Together, we found that consumers are not only more likelyto purchase a product promoted with a probabilistic free discount over the same product promoted with a surediscount but that they are also likely to purchase more of it. This preference seems to be primarily due to adiminishing sensitivity to the prices. In addition, we find that the zero price effect, transaction cost, and noveltyconsiderations are likely not implicated.

Keywords : perception; gamble; uncertainty; prospect theory; probability weighting; value; Weber–FechnerHistory : Received April 3, 2012; accepted July 26, 2015, by Yuval Rottenstreich, judgment and decision making.

Published online in Articles in Advance.

IntroductionOver the years, a number of retailers have offeredgambling- or lottery-type price discounts to promotetheir sales. For example, a few years ago severalretailers in New England promised full refunds tocustomers who bought their items in the few weeksleading to the Super Bowl and World Series in theevent that the Patriots or the Red Sox, respectively,won. In the case of Jordan’s Furniture, the retailertook in 30,000 orders during the almost 6-week pro-motion period in 2007, and one customer, who tookadvantage of the promotion to buy furniture for hisentire house, ended up getting back $40,000 becausethe Red Sox won the World Series (Reed 2007). Simi-larly, a family-run appliance store retailer in Worcesterthat linked its promotion to the win of the Patriots inthe Super Bowl 2008 expected that the gambling-typediscount would account for 20%–30% of its businessin that year (Sanders 2008). These conditional pricepromotions were by design ambiguous in terms oftheir probability of occurring.

Most recently three separate retail chains inGermany (Real, a “hyper-store” chain similar to Wal-mart in the United States; Mann Mobilia XXXL, one ofthe biggest furniture store chains; and Media Markt,the leading consumer electronics retailer, similar to

Best Buy in the United States) ran one-week promo-tions announcing that every 100th and 10th purchase,respectively, would be free. In case of the MediaMarkt campaign in 2010, the probabilistic free pricepromotion, with its unambiguously defined probabili-ties, was determined at the end of day of the purchaseand needed to be cashed in stores within 14 days ofthe purchase date (see Figure 1).

The retailers mentioned above seem to share theintuition that a gambling- or lottery-type of price pro-motion is attractive to consumers, which might bebased on the observation that consumer spending ongambling, including lotteries, is a multibillion-dollarindustry (e.g., $98 billion in the United States; IBIS-World 2013) that continues to show solid growth. Thisattraction to risk can in part be attributed to wish-ful thinking and wishful betting, the tendency to beoveroptimistic that a desirable future outcome (thebig prize) will occur and to bet more aggressively onit (Bar-Hillel and Budescu 1995, Seybert and Bloom-field 2009, Trope et al. 1997).1

1 See Ailawadi et al. (2014) for a recent paper that formulates, esti-mates, and analyzes a model of consumer response to conditionalnonfree discounts (i.e., there is no chance to get something forfree) with ambiguous probabilities linked to a popular sports event

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Mazar, Shampanier, and Ariely: When Retailing and Las Vegas Meet2 Management Science, Articles in Advance, pp. 1–17, © 2016 INFORMS

Figure 1 (Color online) Media Markt’s Advertised Probabilistic PricePromotion, Offering Every 10th Purchase for Free

Notes. Translation from German:Focal message: “Every 10th purchase for free! The last digit of a receiptnumber = Winning number.”Picture of receipt on the bottom left, text above the arrow pointing on thereceipt: “Here you find the winning number.”Text in the yellow banner to the right of the receipt: “This is how easy it isgo get your money back: With the correct last digit of your receipt number,your purchase is for free! Only until January 9! The daily winning number:after 22:30 o’clock on mediamarkt.de and on the phone at 0800/800 70 60.”Disclaimer in small black font under the yellow banner focuses first on phoneand Internet service contracts as well as warranties that are excluded fromthis promotion and then states: “The winnings need to be picked up within14 days after date of your purchase.”Source. Used with permission from Media-Saturn-Holding GmbH.

Despite such intuitions, the vast majority of promo-tions are not probabilistic, suggesting that the beliefin such pricing mechanisms is far from universal.In addition, it is also unclear how such probabilis-tic price promotions that offer something for free(probabilistic free price promotion) compare with the

occurring (versus sure discounts). Ailawadi et al. (2014) find thatthe response to such conditional promotions is highly segmentedand related among others to perceived thinking costs, saving ben-efits, and entertainment benefits, as well as to event involvementand gambling proneness, the latter two of which in particular affecta consumer’s estimate of the likelihood of the event occurring.

ubiquitous traditional sure price promotions (Hanet al. 2001) if the latter offered a fixed discount ofequal expected monetary value. That is, it is unclearwhether and why customers would be more, less, orequally attracted to shopping at a store that offered,e.g., a 10% chance to get their purchases for free (witha 90% chance to pay the regular price) when there areother stores that carry the same items but offer themat a guaranteed, fixed percentage off. Similarly, theremay be situations where a retailer (e.g., Kayak.com)sells products (e.g., hotel rooms) by some supplierswith a price promotion and other suppliers without aprice promotion, and it is unclear if and why a prob-abilistic free price promotion may be more success-ful in shifting the market share of the correspondingproduct than would a sure price promotion. Thesequestions are highly relevant to marketers (retailersand suppliers alike) who may want to promote someproducts or stores over others.

In this paper we investigate under controlled con-ditions whether, to what extent, and why for plannedpurchases a probabilistic free price promotion is pre-ferred to a sure price promotion of equal expectedmonetary value (i.e., discount) when the probabili-ties are unambiguously defined (similar to the MediaMarkt example from Germany mentioned above) andthe discount immediately determined and paid out atcheckout. Across six experiments we find that sucha probabilistic free price promotion is indeed moreattractive. Furthermore, the preference for the prob-abilistic free price promotion is fairly robust acrossvarious probabilities of wining and across variousproduct price levels. Finally, we show that this prefer-ence is not driven by an attraction to a zero price, anaversion to transaction cost, or novelty, but rather pri-marily due to a diminishing sensitivity to the prices.

Standard Rational Fundamentals:Expected Utility TheoryStandard expected utility theory predicts that con-sumers are risk averse2 and will thus prefer the sureprice promotion over a probabilistic free price promo-tion of equal expected value. For very small stakes,consumers have been shown to be risk neutral (Rabin2000), which would imply indifference between thetwo promotions. Thus, depending on the magnitudeof the stakes, we expect either indifference or a pref-erence for sure discounts.

2 Although traditionally the terms “risk aversion’’ and “risk seek-ing’’ are used to describe concavity and convexity, respectively, ofthe utility function, we use these terms to refer to their resultingchoice properties. For example, “risk seeking’’ refers to an observedpreference for a risky option over a sure option of equal expectedmonetary value.

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Mazar, Shampanier, and Ariely: When Retailing and Las Vegas MeetManagement Science, Articles in Advance, pp. 1–17, © 2016 INFORMS 3

Behavioral FundamentalsFrom a behavioral decision theory perspective, thedifferences between the two types of price promotioncan give rise to several types of psychological pro-cesses. Moreover, because of the multitude of thesepotential psychological processes, it is not clear howthe two types of price promotion will translate into apreference of one type of promotion over the other.

Factors Favoring the Sure Price PromotionUncertainty Effect. The “uncertainty effect” (Gneezy

et al. 2006) posits that, because we dislike uncertainty,individuals value a risky gain prospect less than itsworst possible outcome (i.e., direct risk aversion; seeNewman and Mochon 2012, Simonsohn 2009). Thatis, according to the uncertainty effect, people valuethe probabilistic free price promotion with its twopossible outcomes (best possible outcome, free; worstpossible outcome, paying the regular price) less thanpaying the regular price. As a result, individuals areexpected to value the probabilistic price promotionless than the sure nonfree price promotion of equalexpected discount and act accordingly.Certainty Effect. Similar to the uncertainty effect,

the “certainty effect’’ as coined by Kahneman andTversky (1979, p. 265) posits that “people overweightoutcomes that are considered certain, relative to out-comes which are merely probable” (for all 0 < p < 1,�4p5+�41 − p5 < 1). Thus, both the uncertainty effectand the certainty effect predict that consumers wouldprefer a sure price promotion over a probabilisticprice promotion.

Factors Favoring the Probabilistic FreePrice PromotionZero Price Effect. One factor that could favor the

probabilistic price promotion is the attraction to zeroprices. Previous research has shown that promotionsthat offer something for free are likely to be evalu-ated differently (Chandran and Morwitz 2006, Nunesand Park 2003, Palmeira 2011) than nonfree promo-tions. Building on this work, Shampanier et al. (2007)found that people experienced significantly more pos-itive affect when facing a free offer (the price equals$0) compared with other price offers (e.g., the priceequals $0.01 or $0.02), and this disproportionatelypositive affect led to a larger demand for zero-pricedproducts than what standard cost-benefit analysiswould have predicted. In line with this account, indi-viduals may find the probabilistic free price pro-motion more attractive than a sure price promotionbecause the former includes an additional positiveelement, which is the possibility of getting somethingfor nothing. It is important to note that one other pre-diction of this account is that the attraction to the

probabilistic free price promotion should be indepen-dent of the price level or the probability p of winningthe product for free (which we test directly).

Transaction Cost. Similarly to the zero price effect,hassle or transaction cost considerations would favorthe probabilistic free price promotion. This is becausewinning the probabilistic free price promotion avoidsthese costs—there is no need to take out one’s walletand pay.

Novelty. Another factor that could favor the prob-abilistic price promotion is novelty. Customers mayfind probabilistic price promotions particularly ap-pealing simply because they have had no previousencounter with such promotions (for novelty as anarousal-inducing stimulus that increases individuals’probability of self-exposure to it, see, e.g., Berlyne1970). As with the zero price effect and an aver-sion to transaction cost, this factor should lead to anattraction to the probabilistic price promotion that isindependent of the price level or the probability p ofwinning the product for free.

Diminishing Sensitivity. Another set of predictionscan be made based on diminishing sensitivity. As dem-onstrated by Tversky and Kahneman’s (1981) seminalexperiment, when participants were asked whetherthey would travel 20 minutes to purchase a calculator[jacket] typically priced at $15 [$125] on sale for $10[$120], they were more willing to travel the 20 min-utes for the same $5 discount for the cheaper calcu-lator than for the more expensive jacket. This findingshows that, when evaluating a sure discount, peo-ple compare the discounted price to the regular, fullprice and behave in a Weber–Fechnerian way (Stigler1965); that is, people display diminishing sensitivityas prices increase, a basic psychophysical principlethat is reflected, e.g., in the concavity of prospect the-ory’s gain value function (v4x5 = x�, for x ≥ 0, with�< 1 (see also Thaler (1980)).

Therefore, if individuals display diminishing sensi-tivity to prices, the perceived value of the sure dis-count is the difference in perceived magnitude of theregular, full price versus the discounted sure price:

V4Sure discount5= 4Regular price5�

− 4Discounted sure price5�0 (1)

In a situation in which a customer is choosing be-tween a sure price promotion and a probabilistic pricepromotion of equal expected value, and where theprobabilistic price promotion offers a chance p to notpay anything (i.e., “winning”), from (1) it follows that

V4Sure discount5 = 4Regular price5�

− 441 − p5× 4Regular price55�

= 41 − 41 − p5�5× 4Regular price5�0 (2)

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Although the evidence on how individuals perceivesure price promotions is rather convincing (Tverskyand Kahneman 1981), it is an open question how indi-viduals may perceive the value of probabilistic pricepromotions (i.e., what happens under uncertainty). Ifindividuals perceive them in a similar way to the wayin which they perceive sure price promotions (i.e.,they focus on the magnitude of the prices), we wouldexpect the value of the probabilistic discount to be

V4Probabilistic discount5= 4Regular price5�−p×4Discounted probabilistic price5�

−41−p5×4Regular price5�0 (3)

For probabilistic free price promotions (i.e., the dis-counted probabilistic price = $0) it follows that

V4Probabilistic free discount5

= 4Regular price5� − 41 − p5× 4Regular price5�

= p× 4Regular price5�0 (4)

From this it follows that

V4Sure discount5 < V4Probabilistic free discount51for all 0 < p < 1 and �< 103 (5)

With these assumptions, individuals should alwaysprefer a probabilistic free price promotion to a sureprice promotion of equal expected value. In otherwords, if we assume that individuals display dimin-ishing sensitivity and we are dealing with probabilis-tic promotions that include the chance p of getting thepurchase for free (otherwise 41 − p5 chance of payingthe regular price), then we would expect individu-als to attach a greater value to the probabilistic freeprice promotion than to the sure price promotion ofequal expected value. This would hold true indepen-dent of the price level (i.e., for all �< 1: V(Probabilisticfree discount)/V(Sure discount) > 1). Further, the pref-erence for the probabilistic free price promotion, mea-sured as the ratio V(Probabilistic free discount)/V(Surediscount), is decreasing as the probability of gettingthe product for free increases (i.e., p → 1). The solidline in Figure 2, panel A depicts the preference ratioand Figure 2, panel B depicts the difference betweenthe two price promotions’ values for diminishing sen-sitivity �= 0088 (see parameter estimation in Tverskyand Kahneman 1992).Diminishing Sensitivity and Probability Weighting. A

modification to diminishing sensitivity could comefrom adding a component based on the probability

3 Equation (5) is true if and only if 1 − 41 − p5� < p, which is equiv-alent to 1 − p < 41 − p5�, which is true for all 0 < p < 1 and �< 1.

Figure 2 (Color online) Predicted Attraction to the Probabilistic Freeover the Sure Price Promotion

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Diminishing sensitivityDiminishing sensitivity and weighted probabilities

Note. Panel A shows the value ratios, which are independent of price levels.Panel B shows the value differences for a product with a regular price of $10.

value function of Kahneman and Tversky’s (1979)prospect theory. Specifically, Kahneman and Tver-sky (1979) describe decision weights of probabili-ties �4p5 such that small probabilities are generallyoverweighted (�4p5 > p; the probability weightingfunction is concave) and large probabilities are under-weighted (�4p5 < p; the probability weighting func-tion is convex). The dashed line in Figure 2, panel Adisplays the predicted preference ratio of the prob-abilistic free price promotion to the sure price pro-motion based on Prelec’s (1998, p. 505) probabilityweighting function �4p5 = exp6−� × 4− ln p5�7, with� = 1 and � = 0065, and with diminishing sensitiv-ity � = 0088 (see the parameter estimation in Tver-sky and Kahneman 1992); Figure 2, panel B depictsthe difference of the two price promotion’s values.As can be seen, with these parameter assumptions,individuals should attach a greater value to the prob-abilistic price promotion over the sure price promo-tion of equal expected value for most probabilities.Another prediction of this perspective is that the pref-erence for the probabilistic price promotion, measuredas the ratio V(Probabilistic free discount)/V(Sure dis-count), is decreasing as the probability of getting theproduct for free increases (i.e., p → 1). Unlike the

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case with dimishing sensitivity only (i.e., no decisionweights), the decrease is much sharper. Yet anotherprediction of this perspective is that the preferencewill reverse (i.e., V(Probabilistic free discount)/V(Surediscount) < 1) to a preference for the sure price pro-motion for p > 0076.

Previous Consumer Behavior Researchon Probabilistic PromotionsThe literature most relevant to the work presentedhere is on ambiguity. Specifically, most recently, Gold-smith and Amir (2010) focused on sales promotionsthat promised that consumers would either receive aless valued product gift (bag of unpopped popcorn)or a more valued product gift (a can of soda) withthe purchase of a candy bar, without disclosing theprobabilities of receiving either gift. In their incentive-compatible experiment in an on-campus snack shop,Goldsmith and Amir (2010) observed a higher pur-chase rate for the promoted candy bar when thegift was more valued than when it was less valued.More importantly, the purchase rate of the candy bar,when coupled with a promotion that was ambigu-ously defined as either of the two (less or more val-ued) gifts, did not differ from when coupled with amore valued gift promotion (the three types of pro-motions were run separately, one condition at a time).The authors suggested that their findings were due towishful thinking, which made customers focus on thebest option of the ambiguously defined promotion.Extrapolating Goldsmith and Amir’s (2010) findingsfrom the product promotions domain to our price pro-motions domain and from unknown to known prob-abilities, a probabilistic price promotion that offered,e.g., a 10% chance to get a purchase for free anda 90% chance to pay the regular price would causeconsumers to focus on the best possible outcome(“free”). As a consequence, such a probabilistic pricepromotion would be as effective and thus cheaperfor a retailer than simply offering a product for freewith certainty. That is, individuals would value therisky prospect the same as its best possible realiza-tion, a conclusion that may not be intuitive and isin opposition to the prediction of the uncertaintyeffect. However, if true, then a probabilistic discountwould also be superior to a certain discount of equalexpected monetary value (e.g., 10% off the regularprice for sure).

In other related work Dhar et al. (1995; see also1999) tested in an incentive-compatible experimentin an on-campus store whether an imprecisely statedprice promotion (e.g., “around X% off”) was moreor less successful in increasing the market share ofa candy bar than a precisely stated price promo-tion (“X% off”), (Dhar et al. (1995, 1999) ran one

type of promotion at a time). Although not the mainfocus of their work, their three precise discount-conditions (“20% off” versus “25% chance of sav-ing 80%” versus “80% chance of saving 25%”) allowfor the equal expected monetary value-type of com-parison on which we are focusing. Interestingly, andunlike the extrapolation from Goldsmith and Amir’s(2010) findings, Dhar et al. (1995, 1999) found a nulleffect. That is, they found no significant differencein the market shares of a candy bar when offeredwith any of these three price promotions, implyingthat probabilistic price promotions do not differ intheir attraction from sure price promotions of equalexpected monetary value or discount.

Overview of ExperimentsGiven the mixed predictions based on existing theo-ries as well as findings from previous research in mar-keting, it is unclear if, how, and why a probabilisticprice promotion with a chance to get one’s purchasefor free differs from a sure price promotion of equalexpected monetary value—questions that should be ofimportance for marketers that are trying to improveon their price promotion strategies. The current paperaddresses this question for planned purchases througha series of four incentive-compatible experiments inthe field (Experiments 1, 2, and 3) and in the lab-oratory (Experiment 4) and two hypothetical onlineexperiments (Experiments 5a and 5b) across productsof varying regular, full-price levels ($0.75 to $200). Thepaper concludes with a discussion of the theoreticaland practical implications and its limitations, as wellas several potential directions for future research.

The general set-up in Experiments 1–4 was suchthat we offered consumers a choice between a prob-abilistic price promotion and a sure price promotionof equal expected monetary value (joint valuation set-ting) at the point of purchase, and we measured thepercent of purchases made with a probabilistic pricepromotion choice. In Experiments 5a and 5b, promo-tions were offered separately (separate valuation set-ting), one at a time, and we measured the percentof purchases made (traffic) as well as the averageconsumer demand (basket size). Except for Experi-ment 1, we presented participants with the followinginformation:4

—for the probabilistic price promotion: p% chanceof paying the discounted probabilistic price (e.g., $0)and 41 − p5% chance of paying the regular price;

—for the sure price promotion: 100% chance of pay-ing the discounted sure price, that is, p% off the reg-ular price.

4 In all experiments, except for Experiment 1, probabilities were pre-sented as percentages. The discounted probabilistic free price wastypically presented as both $0 and “free.”

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In addition, we randomized the order in which wepresented offers. Unless reported otherwise, no con-ditions, measures, or subjects were dropped from theexperiments reported in this paper.

Experiment 1: Vending MachineFor our first experiment we purchased a vendingmachine (see Figure S1 in Supplementary Materialsand Methods, available at http://dx.doi.org/10.1287/mnsc.2015.2328) that we placed next to two exist-ing vending machines centrally located in a studentlounge where they were frequented by students, fac-ulty, and staff members on a regular basis. Our vend-ing machine had 10 buttons for candies. We stackedthe vending machine with five types of candy, withtwo buttons each: Snickers, M&M’s, Twix, 3 Mus-keteers, and Starburst. The vending machine wasopaque (individuals could not see the inside), and thecandies were represented with a picture and a priceplaced next to each of the 10 buttons. All candiesretailed at a regular, full price of $0.75 (the same asthe candies in the other two vending machines in thelounge). A candy’s price also appeared on the displaywhen people pressed a button. The vending machinecould sell only one candy at a time.

ProcedureWe manipulated the prices for the candy over timeand recorded the sales volume. Our experiment con-sisted of three two-week periods. For the first twoweeks (“before period”) and the last two weeks(“after period”), we offered the candy at the regu-lar price of $0.75 each. Between these two periodswe ran a two-week sales promotion in which weoffered two different types of price promotion: A sureprice promotion offering 33% off the regular price(consumers had to pay a discounted sure price of$0.50 for a candy) and a probabilistic price promo-tion that required consumers to first pay the regularprice $0.75 for a candy but offered a 33% chance to gettheir money back when the candy was released (themoney was wrapped around the candy).5 Both typesof promotions offered an expected discount or “gain”of $0.25. The two promotions were offered simulta-neously with a sign prominently displayed at eyelevel on the front of the vending machine announcingand color-coding both types of promotion (see Fig-ure 3). Since each type of candy occupied two but-tons of the vending machine, one button (with a greensticker) represented the sure price promotion and theother button (red sticker) represented the probabilisticfree price promotion. Thus, consumers could decide

5 The vending machine was stocked to produce a random sequencefor the probabilistic discount as opposed to, for example, a freecandy every third purchase.

Figure 3 (Color online) Vending Machine Sign Announcing thePromotions in Experiment 1

which promotion they wanted by pressing the corre-sponding button (for more details, see SupplementaryMaterials and Methods).

Results and DiscussionFirst, the promotion proved very successful: sales in-creased from 83 candies in the “before period” to204 candies during the promotion period. After ourpromotion ended, sales in the “after period” wentback to 81 candies. Second and more importantly, dur-ing the promotion period we sold almost 50% morecandy with the probabilistic price promotion (120 can-dies) compared to sales with the sure price promo-tion (84 candies). In other words, of the 204 candiessold during the promotion period, 59% were pur-chased with the probabilistic free promotion and 41%were purchased with the sure promotion, and thisratio was significantly different from an equal split(�2411N = 2045= 60353, p = 00012).6

Experiment 2: Differing Probabilities ata Local Video StoreOur first experiment with the vending machine showsthat, when offered a choice between the two typesof promotion, consumers are more likely to choosethe probabilistic (risky) free price promotion than thetraditional, sure price promotion. Next, we examinedthe robustness of the attraction to the probabilisticfree price promotion across a range of probabilitiesand with a higher-priced product for which the pricesand discounts are less likely considered “peanuts.”Previous research (see, e.g., Prelec and Loewenstein1991, Weber and Chapman 2005) has shown that for

6 We are assuming independence of observations for the �2 test but,in actuality, we were not able to track and thus ensure that each ofour purchase observations was made by a unique customer.

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small-stakes gains with at least medium probabili-ties (p > 10%) to win, people become less risk aversethan for large-stakes gains. Furthermore, for suffi-ciently small gains of less than $1, Markowitz (1952)posited that people might even become risk seeking.7

Thus, if we found that, for choices where the sure dis-count was greater than $1, we continued to observean attraction to the probabilistic free price promotion(i.e., significantly more than 50% choose it), the find-ings could be less likely considered an artifact of the“peanuts” effect.

In addition, given the promotional sign on thevending machine, we might have attracted some con-sumers that originally did not intend to purchase acandy. Similarly, some of the higher sales volume forprobabilistic free price promotion candy in Experi-ment 1 could have been caused by individual cus-tomers purchasing more than one candy due to the“windfall” of getting a candy for free (i.e., customersmaking additional unplanned purchases on top oftheir planned purchase rather than the probabilisticfree price promotion attracting more of the plannedpurchases than the sure price promotion). Thus, weattempted to replicate our findings in a more con-trolled setting where we could limit the quantity eligi-ble for discount to one item per customer and ensurethat customers learned about the promotions onlywhen they were at the checkout counter. For this pur-pose, we conducted our experiment at a local videorental store where a DVD rental cost $4.50.

ProcedureThree hundred and twenty-five customers in a localvideo rental store were informed at checkout by ex-perimenters disguised as staff that the store had aspecial price promotion valid for one DVD movie percustomer. Customers were told that they could choosebetween two types of price promotion, a sure promo-tion and a probabilistic promotion, and that if theychose the probabilistic promotion they would have toroll a die in order to find out if they had to pay $0 (dis-counted probabilistic price) or $4.50 (regular price).

Using either a 6-sided or 10-sided die, we manipu-lated the probabilities of winning between customerson five different levels: 10%, 33%, 50%, 67%, and90%, with the expected discounts $0.45, $1.50, $2.25,$3, and $4.05, respectively (see Table 1). The condi-tions were run one at a time, one hour each, with a30-minute break between conditions. By design, theexperimenters knew which condition they were run-ning at any given point in time but they were not

7 As Weber and Chapman (2005) report, it is not clear whether peopleactually become risk seeking. Further, risk seeking is not a necessaryrequirement of the “peanuts’’ effect (Prelec and Loewenstein 1991).

aware of any hypotheses. The experiment was con-ducted over several days. Each day included all theconditions in a randomized order.

Results and DiscussionThe percentages of customers choosing the probabilis-tic price promotion rather than the sure price pro-motion are presented in Figure 4, and the �2 testresults for the difference from an equal split are pre-sented in Table 1. As can be seen, contrary to whatstandard rational fundamentals and the uncertaintyand certainty effects would predict, the probabilisticfree price promotion attracted significantly more cus-tomers than the sure price promotion at all levels butone discount level: all the way up to and includingp = 67% (customers’ choice between the two promo-tions at the p = 90% level was not significantly differ-ent from an equal split). First, these results replicatethe findings from Experiment 1 for a more expensiveproduct and over a wider range of probabilities withexpected discounts greater than $1 (i.e., for p > 10%).Thus, we conclude that our findings are less likely anartifact of the “peanuts’’ effect (Prelec and Loewen-stein 1991).

Second, we observed a general decrease in the at-traction to the probabilistic price promotion relative tothe sure price promotion as the probabilities of win-ning and the expected discounts increased (nominallogistic regression parameter estimate for probabilitylevel p as continuous variable B = −101, SE = 0043,�2 = 6048, p = 0001). This downward-sloping trendcounters the zero price effect, transaction cost, andnovelty effects as sole drivers of the attraction tothe probabilistic free price promotion, because eachof those explanations would require the attraction toremain constant across probability levels.

Third, the facts that we do not see a sharp decline inthe attraction of the probabilistic free price promotion

Figure 4 (Color online) Observed Preference for the ProbabilisticFree Price Promotion Over the Equal Expected Value SurePrice Promotion for a DVD Rental at a Regular Price of$4.50 in Experiment 2

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Table 1 Customers’ Choices Between the Probabilistic Free and Sure Price Promotions in the Five Between-SubjectsConditions in Experiment 2

Customers choosingProbabilistic free price the probabilistic free

Condition (%) promotion prices Sure price promotion price price promotion (%) �2 (df, N) p-value

10 10% 2 $0 $4.05 76 190059 <0000190% 2 $4050 (10% off $4.50) (1, 68)

33 33% 2 $0 $3 68 80067 0000567% 2 $4050 (33% off $4.50) (1, 60)

50 50% 2 $0 $2.25 68 80727 0000350% 2 $4050 (50% off $4.50) (1, 66)

67 67% 2 $0 $1.50 66 60452 0001133% 2 $4050 (67% off $4.50) (1, 62)

90 90% 2 $0 $0.45 55 00710 0039910% 2 $4050 (90% off $4.50) (1, 69)

Note. The test results indicate the probability that the percent of customers choosing the probabilistic free price promotion is differentfrom the 50% chance level; df, degrees of freedom.

and that we do not observe any probability level pat which people significantly prefer the sure pricepromotion over the probabilistic free price promo-tion suggest that individuals’ preferences are largelyaffected by a diminishing sensitivity to the prices andless so by decision weights (compare results in Table 1and Figure 4 to those in Figure 2).

The following two experiments further examinepossible causes underlying the apparent boost to peo-ple’s risk seeking in purchases with probabilistic freeprice promotions.

Experiment 3: Zero as a Special Priceand Transaction CostExperiment 3 was designed to test if customers’ at-traction to the probabilistic free price promotion wasboosted at all by positive affective utility associ-ated with a free offering or by an aversion to trans-action cost. Following the experimental design ofShampanier et al. (2007), we set out to test this possi-bility by comparing the attraction to the probabilisticprice promotion across conditions in which the bestpossible outcome of the probabilistic price promotioneither involved a chance to get something for free (dis-counted probabilistic price = $0) or a chance to pay asmall but relatively insignificant amount (discountedprobabilistic price > $0). If the attraction to the proba-bilistic price promotion is driven solely by the affectiveutility associated with a zero price or lower transactioncost due to a chance of not having to pay, the attractionshould be significantly lessened or eliminated once thebest possible outcome of the probabilistic price pro-motion does not offer a chance of getting the productfor free but requires paying a small price.

ProcedureThe experiment was conducted at the same localvideo rental store and with a similar procedure as

in Experiment 2. That is, customers were informedat checkout by experimenters disguised as staff thatthe store had a special promotion valid for one DVDmovie per customer (regular price = $4050) and thatthey could choose between two types of promotion:a sure promotion that guaranteed a discounted sureprice of $4 (i.e., 11% or $0.50 off the regular price)and a probabilistic price promotion. The probabilisticprice promotion was presented as one of the follow-ing, depending on the condition:8

(1) 11% chance to pay a discounted price of $0 and89% chance to pay the regular price of $4.50,

(2) 12% chance to pay a discounted price of $0.38and 88% chance to pay the regular price of $4.50, or

(3) 13% chance to pay a discounted price of $0.69and 87% chance to pay the regular price of $4.50.That is, we manipulated the chance of winningthe probabilistic price promotion between customerson three different levels (p = 11%, 12%, and 13%,respectively) while keeping the expected value of thediscounts at $0.50 across all three levels (unlike inExperiment 2 where the expected value of the dis-count increases as p increases) and across both theprobabilistic and sure price promotion options.

The three conditions were run one at a time, onehour each, with a 30-minute break between condi-tions. The experiment was conducted over the courseof one day with 163 customers. The order of the con-ditions was randomized and the probabilistic pricepromotion was carried out by having customers“pull” the handle of a digital slot machine on a laptop.

Results and DiscussionIndependent of whether the probabilistic price pro-motion offered a chance to get the DVD for free

8 As a result of rounding, the expected values of the probabilisticprice promotions are not exactly $0.50. They are $0.495 in condi-tion 1, $0.494 in condition 2, and $0.495 in condition 3.

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or not, customers significantly preferred the proba-bilistic price promotion over the sure price promo-tion: 73% (p = 11% free condition 1: �2411N = 555 =

110364, p < 00001), 75% (p = 12% nonfree condition 2:�2411N = 555 = 130255, p < 00001), and 77% (p = 13%nonfree condition 3: �2411N = 535= 150868, p < 00001).More importantly, we compared the percentage ofcustomers choosing the probabilistic price promotionover the sure price promotion across the three con-ditions. A nominal logistic regression revealed nosignificant difference between the three conditions(�2421N = 1635= 00313, p = 00856, R2 = 00002).

One possible explanation of our findings is thatthe two discounted probabilistic nonzero prices ($0.38and $0.69) were perceived as zero prices. However,given that the zero price effect was shown for the dif-ference between $0 and $0.01 (Shampanier et al. 2007),this explanation does not seem likely. Rather, we inter-pret our findings to suggest that the preference for theprobabilistic free price promotion is substantial andnot dependent on the attraction of a zero price or anaversion to transaction cost.

Figure 5 displays predictions based on only dimin-ishing sensitivity � = 0088 (Tversky and Kahneman1992) as well as diminishing sensitivity � = 0088 andPrelec’s (1998) probability weighting function �4p5 =

exp6−� × 4− ln p5�7, with � = 1 and � = 0065. Focus-ing on the preference ratios depicted in Figure 5,panel A, a surprising observation to make again isthat the slope of our findings may be better explainedby diminishing sensitivity to prices without weightedprobabilities.

Experiment 4: Replication and NoveltyExperiment 4 conceptually replicates Experiment 2with several extensions. First, it examines the general-izability of the attraction of the probabilistic free pricepromotion to a more expensive product, a rOtringpen sold at a regular, full price of $10. Second, ittests a more fine-grained set of probabilities of win-ning the probabilistic free price promotion (13 p-levelsfrom 5% to 95%) to further support the shape of theattraction to the probabilistic price promotion curveobserved in Experiment 2. Third, it contrasts individ-uals’ choices between the probabilistic free and sureprice promotions with their choices between riskymonetary gain gambles and sure monetary gains ofequal expected surplus. Fourth, this experiment wasrun in the laboratory as a within-subject design, withone of the participants’ decisions actually carried out,to assess whether the attraction to the probabilisticfree price promotion in any way received a boostfrom being novel to some individual participants.Work by Berlyne (e.g., Berlyne 1970, Berlyne andParham 1968) suggests that novelty as an arousal-inducing stimulus and its hedonic value decrease in

Figure 5 (Color online) Predicted Attraction to the 11% ProbabilisticFree and 12% and 13% Probabilistic Nonfree PricePromotions Over the Sure Price Promotion in Experiment 3

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Probability of “winning” the probabilistic price promotionfor the DVD rental

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Notes. The exepcted discount was held constant at $0.50. Panel A showsthe value ratios, and panel B shows the value differences for a regular priceof $4.50.

the face of prolonged repetition of exposure to thenovel stimulus and its preference judgment. In fact,recent work by Dijksterhuis and Smith (2002) showsthat affective adaptation even happens with sublimi-nal exposure. Thus, although a probabilistic free pricepromotion may have been novel to participants at thebeginning of the series of preference judgments, wewould expect novelty and its resulting attraction tothe probabilistic free price promotion to decline overthe duration of the experiment as a result of affectiveadaptation.9

9 Given the work by Berlyne (e.g., Berlyne 1970, Berlyne andParham 1968), as well as Dijksterhuis and Smith (2002), it is reason-able to argue that our participants would experience affective adap-tion even without each decision actually being played out beforethe onset of the next trial. That is, for affective adaption to happen,it is not necessary for participants to experience winning or losingwith the probabilistic free price promotion before they make thenext decision.

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ProcedureThe computer-based experiment was part of a one-hour experimental session consisting of several stud-ies. The payment for participation in the sessionwas $10. According to the recruiting flyer and consentform, participants expected to leave the session withan average compensation of $12–$18 in cash and/orin kind and knew they could withdraw from partici-pation at any point during the experimental session.

The experiment started with a screening questionasking participants whether they were interested inthe possibility of actually purchasing either a rOtringpen worth $10 [pictures of the pen in different colorswere displayed on the screen] or a $10 gift certificatefor Amazon.com [a picture of the gift certificate wasdisplayed on the screen] with their own money. Onlyparticipants who indicated interest proceeded to theexperiment. Eighty-two students participated in thisexperiment.

The instructions of the experiment explained thatparticipants would face 52 decisions and that, at theend of the experiment, one of the 52 decisions wouldbe randomly selected and their choice for that deci-sion would actually be carried out. Participants werepresented with 52 choices each between a risky optionand a sure option (of equal expected value) in termsof a price promotion on the purchase of a $10 rOtringpen, a price promotion on the purchase of a $10 giftcertificate for Amazon.com, monetary gains of up to$10, or monetary losses of up to $10. For each ofour four stimuli (pen, gift certificate, monetary gain,monetary loss) we varied the probabilities of “win-ning” the risky option on 13 levels (i.e., p = 5%, 10%,20%, 30%, 33%, 40%, 50%, 60%, 67%, 70%, 80%, 90%,95%). For example, for the p = 60% level price pro-motions domain, participants were offered a choicebetween a probabilistic free price promotion with a60% chance of paying $0 [41 − p5 = 40% chance ofpaying the regular price of $10] and a sure price pro-motion that required paying $4 [i.e., 60% off the reg-ular price of $10]. For the 60% level monetary gaindomain, participants were offered a choice betweena gamble for a monetary gain with a 60% chanceof getting $10 [41 − p5 = 40% chance of getting $0]and a sure monetary gain of $6. The expected sur-plus/discounts in these two choice sets were thesame, $6. Figure 6 displays prospect theory’s predic-tions for the monetary gain domain (assuming dimin-ishing sensitivity � = 0088 and probability weightingwith �4p5= exp6−1 ∗ 4− ln p500657 applied to all gains).As can be seen, prospect theory predicts that partici-pants prefer the probabilistic monetary gain over thesure monetary gain for small probabilities. Their pref-erence, however, is expected to decline quickly, andfor p > 24054%, we expect a preference reversal with a

Figure 6 (Color online) Prospect Theory’s Predicted Attraction to theProbabilistic Monetary Gain over the Sure Monetary Gain inExperiment 4

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preference for the sure monetary gain over the prob-abilistic monetary gain for medium and large proba-bilities. Thus, for most probabilities we expect to findlower risk seeking for monetary gains than for pur-chases with a price promotion (compare Figure 6 andFigure 2).

The 52 decisions were split into 4 blocks of 13 bystimuli. The blocks were randomized in order, as wellas the 13 decisions within each block. In addition, wecounterbalanced between subjects whether the riskyoption was displayed to the left or right side of thesure option. The entire experiment had a 4 (stimuli)×13 (probabilities) within-subject randomized-blockdesign. In the following, we focus on only 26 deci-sions: the 13 decisions about the purchase of therOtring pen and the 13 decisions about monetarygains. For a full account including all four within-subject conditions, see Supplementary Materials andMethods.

ResultsFigure 7 displays the percentage of participants choos-ing the risky option over the sure option (i.e., theirrisk seeking) on each of the 13 probability levels forthe two domains (rOtring pen with price promotion

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Figure 7 (Color online) Observed Risk-Seeking Behavior Across thePen Purchase-with-Price Promotion Domain and theMonetary Gain Domain in Experiment 4

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as well as monetary gain). As can be seen, for eachof the 13 probability levels, despite equivalent ex-pected surplus, participants were more risk seekingin the price promotion domain than in the monetarygain domain. In addition, the observed risk seekingfor the monetary gains followed to some extent the

Table 2 Parameter Estimates B for Choice of Probabilistic/Risky Option Including Wald Tests of Intercept andSlope Parameter Estimates in Experiment 4

B BParameters (Robust SE) Parameters (Robust SE)

Intercepts InterceptsrOtring pen 00799∗∗∗ Novelty 00821∗∗∗

4000405 (pen before Amazon) 4000685Money gain 00644∗∗∗ Prior exposure 00882∗∗∗

4000465 (Amazon before pen) 4000615Slopes Slopes

rOtring pen −00403∗∗∗ Novelty −00038∗∗∗

4000785 4000105Money gain −00637∗∗∗ Prior exposure −00042∗∗∗

4000855 4000115R2 00667 R2 00673No.of observations 2,132 No. of observations 1,066

F 411815 F 411815Parameter comparisons 4p5 Parameter comparisons 4p5

Intercepts InterceptsrOtring pen = Money gain 8072 Novelty = Prior exposure 0043

4000045 4005145Slopes Slopes

rOtring pen = Money gain 6073 Novelty = Prior exposure 00064000115 4008115

Notes. The top left half of the table shows the parameter estimates from a linear regression model with fixed effectsfor respondents with cluster-robust standard errors (N = 82 clusters), choice (0 = sure option, 1 = risky option) as thedependent variable, and assuming domain-specific intercepts and slope parameters over the 13 probability levels. Testparameters on the top right half of the table were estimated from a linear regression without fixed effects because our twoconditions (novelty and prior exposure) are between subjects and thus perfectly correlated with respondents.

∗∗∗p < 00001.

predicted pattern in Figure 6 (for winning probabilityp > 20%, participants no longer preferred the proba-bilistic monetary gain to the sure monetary gain).

The top left half of Table 2 shows the parameterestimates from a linear regression model with fixedeffects for respondents (i.e., a dummy variable foreach participant, excluding one) and cluster-robuststandard errors, choice (0 = sure option, 1 = riskyoption) as the dependent variable, and it assumesdomain-specific intercepts and slope parameters overthe 13 probability levels. The regression model con-stant was excluded. To further support our obser-vation from Figure 7 that participants’ risk-seekingbehaviors differed by domain (rOtring pen purchasewith price promotion and monetary gain), we per-formed pairwise Wald tests comparing the two inter-cept and slope parameter estimates to each other(see the bottom left half of Table 2). The resultsrevealed that the intercept and slope parameter esti-mates for the rOtring pen and monetary gain weresignificantly different from each other, suggestingthat participants’ risk-seeking behavior was indeedhigher for the purchase with a price promotiondomain than for the monetary gain domain despiteequivalence in expected surplus. Further, the same

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Figure 8 (Color online) Observed Preference for the ProbabilisticFree Price Promotion over the Equal Expected Value SurePrice Promotion for the rOtring Pen Offered at a RegularPrice of $10 With or Without Previous Experience withProbabilistic Free Price Promotions in Experiment 4

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as in Experiment 2, all the way up to the winningprobability p = 67% the preference for the probabilis-tic price promotion over the sure price promotion wassignificantly different from an equal 50:50 split (allp-values < 0005); for winning probabilities p ≥ 70%,there was no significant difference from equal 50:50split (all p-values > 003).

Finally, we can examine whether the attraction tothe probabilistic free price promotion for the rOtringpen was boosted by novelty. For that we can takeadvantage of the fact that individuals made 2 (blocks:rOtring pen and Amazon.com gift certificate) × 13(probabilities) repeated choices in the price promo-tions domain and examine participants’ risk seekingfor the rOtring pen purchase when its block camebefore (i.e., novelty, N = 494) or after (i.e., previousexposure, N = 572) having encountered the proba-bilistic price promotion block for the Amazon.com giftcertificate. As can be seen in Figure 8 and the righthalf of Table 2, we did not find support for the novelty(also known as adaption) hypothesis. For the mostpart, it seems that participants’ were equally or lesslikely to choose the probabilistic free price promo-tion for the rOtring pen when this was their first, asopposed to second, probabilistic free price promotionblock encounter. That is, the attraction to the proba-bilistic free price promotion, if at all, increased withmore exposure (see nonsignificant difference of inter-cept and slope parameters in pairwise Wald tests inthe bottom right half of Table 2).

DiscussionTogether, the results of Experiment 4 replicate thefindings from Experiment 2 with a more fine-grainedset of probabilities of winning the probabilistic freeprice promotion and a more expensive product: indi-viduals generally prefer a probabilistic free pricepromotion over an equal expected value sure pricepromotion across a wide range of probabilities.

The downward sloping trend suggests that theeffect cannot be solely due to the zero price effect,transaction cost considerations, or novelty. Addition-ally, the comparison of participants’ choices in the firstversus second free price promotion block encounterfurther demonstrates that novelty is likely not thedecisive factor for the observed attraction to the prob-abilistic free price promotion: participants’ attractiondoes not decrease over the course of the within-subject design with its multiple trials.

The direct comparison of participants’ choices inthe monetary gain domain and the price promotiondomain in Figure 7 shows that participants were sig-nificantly more risk seeking (i.e., more likely to choosethe risky option) in the context of price promotionsthan in the context of monetary gains. Participants’observed behavior for monetary gains largely fol-lowed prospect theory’s predicted pattern (comparedashed lines in Figure 7 and Figure 6). Similarly, thebehavior observed in the price promotion domain canbe sufficiently explained by individuals’ diminishingsensitivity to the prices with or without weightedprobabilities (compare solid line in Figure 7 to solidand dashed lines in Figure 2).

Experiment 5: Separate EvaluationSettingExperiments 1–4, the main focus of this paper, re-vealed that when consumers face a choice (joint eval-uation setting) between a sure price promotion and aprobabilistic free price promotion of equal expecteddiscount for the same product, they overwhelm-ingly choose the probabilistic price promotion (riskyoption).

In what follows, we expand our focus and presenttwo hypothetical experiments with substantially moreexpensive products (hotel rooms sold at a regular, fullprice of $200 per night) in which we examine theeffectiveness of the two types of promotions in sep-arate evaluation settings. That is, we examine theireffectiveness in an indirect choice paradigm with twodifferent products (adopted from Gneezy et al. 2006)where one product is promoted and another prod-uct is not. We do this to broaden the generalizabilityof our findings and examine if, when a companywants to temporarily promote one of their prod-ucts over others (e.g., Procter and Gamble decidingto promote their Pantene shampoos but not theirHerbal Essences shampoos), offering a probabilisticfree price promotion versus a sure price promotionmakes a difference in terms of market shares. Specifi-cally, we test whether the probabilistic free price pro-motion is likely to attract more consumers (increasetraffic; Experiment 5a) and encourage greater spend-ing (basket size; Experiment 5b) than a sure price

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promotion—two measures of great importance formarketers.

The findings from Experiments 1–4 support theconclusion that, when comparing sure and probabilis-tic free price promotions, people focus on the mag-nitude of the prices. In addition, because in thesejoint evaluation settings we offered two types ofpromotion for the same product, the product itselfbecame irrelevant (nondiscriminatory), making pricesand discounts particularly salient. In the new, sep-arate evaluation setting in Experiments 5a and 5b,because we now also make the product become adiscriminatory attribute, the impact of prices anddiscounts relative to the product may be reduced.However, as long as prices and discounts continueto be discriminatory, we would continue to expect anattention to prices and thus, based on our previoustheoretical reasoning with diminishing sensitivity (seethe Behavioral Fundamentals section), higher demandfor the probabilistic free price promotion than the sureprice promotion.

In addition, previous research has shown that jointversus separate evaluation settings change the waypeople evaluate options (Hsee et al. 1991). The under-lying evaluability hypothesis posits that attributesthat are relatively difficult compared to relatively easyto evaluate independently have a lesser impact inseparate than in joint evaluation settings, whereaseasy-to-evaluate attributes remain equally impactful.Our separate evaluation setting in Experiments 5aand 5b removes the comparison price promotion (e.g.,a probabilistic free price promotion product is nowcompared to a nonpromotion product rather than toanother sure price promotion product). Given thatprices and discounts are considered to be relativelyeasy-to-evaluate attributes, they therefore continue tobe salient attributes. Thus, again, we would con-tinue to expect to find the probabilistic free price pro-motion to attract more demand than the sure pricepromotion.

ProcedureFour hundred (Experiment 5a) and five hundred(Experiment 5b) participants in the United Stateswere recruited through Amazon’s Mechanical Turk(MTurk10) in exchange for 30 cents to complete a shortvacation study on Qualtrics.

Participants were randomly assigned to one of fivebetween-subject conditions in which they were askedto imagine that they were going on a seven-day vaca-tion to Spain and were debating between a culturalvacation in the city of Barcelona and a beach vacationin a coastal resort approximately 100 miles south of

10 For an examination of the demographic makeup of MTurk par-ticipants and the quality of the data obtained with that sample, see,e.g., Buhrmester et al. (2011) and Paolacci et al. (2010).

Barcelona. The participants were told that they wenton Kayak.com to compare hotel prices and found onefour-star hotel in Barcelona and one four-star hotel inthe beach resort, both offered at a regular, full price of$200 per night, where they would consider staying at.They were then presented with regular or discountedprices per night for those two hotels and asked inExperiment 5a, to indicate which vacation (Barcelonacity hotel or beach resort hotel) they would choose;in Experiment 5b, they were asked how many of theseven days, if any, they would book at each place.That is, in each condition participants needed to makea decision between the Barcelona city hotel and thebeach resort hotel.

The price per night for the beach resort hotel waskept at the regular, full price of $200 across all con-ditions, whereas the price of the Barcelona city hotelwas varied across conditions to either be $200 (con-trol condition) or discounted such that the expecteddiscount was $20. There were three discounted priceconditions for the Barcelona city hotel: a sure pricepromotion condition with a discounted price of $180;a probabilistic free price promotion condition with a10% chance of not paying anything and 90% chanceof paying the regular, full price of $200; and a prob-abilistic nonfree price promotion condition with a20% chance of paying a discounted price of $100 and80% chance of paying the regular, full price of $200.Finally, we added an exploratory fifth condition inwhich we told participants that the Barcelona cityhotel offered a choice between a sure price promo-tion (with a discounted price of $180) and a 10%probabilistic free price promotion (with a 10% chanceof paying $0 and 90% chance of paying the reg-ular, full price of $200; choice condition). In thisexploratory condition, in Experiment 5b, if partici-pants indicated they wanted to spend one or moredays at the Barcelona city hotel, on the next pagethey were asked to choose between the sure and prob-abilistic free price promotion for the Barcelona cityhotel.11

Participants were randomly assigned to one of thefive conditions. Upon indicating how they wouldwant to spend their seven-day vacation, participantsin both experiments were asked to indicate howmuch, in general, they liked beach vacations and cityvacations (on nine-point scales each), their gender,age, ethnicity, and highest finished degree of educa-tion. The survey ended with an attention questionthat we planned to use to exclude participants ifwrongly answered (for all questions, see Supplemen-tary Materials and Methods).

11 That is, unlike in the other conditions, in this condition partici-pants had to engage in a two-step decision-making process. Thissecond step was not existent in Experiment 5a.

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In what follows we present and discuss our find-ings excluding the exploratory fifth condition. For afull account of the data and results, see Supplemen-tary Materials and Methods.

Experiment 5a: ResultsTable 3 shows the parameter estimates from a nom-inal logistic regression model with choice (0 = beachresort vacation, 1 = Barcelona city vacation, N = 326)as the dependent variable, the sure price promotioncondition as baseline, and the remaining three condi-tions as independent variables (dummy coded with1 = condition, 0 = not this condition). As can be seen,significantly more participants chose the Barcelonacity vacation over the beach resort vacation when theBarcelona city hotel was offered with a probabilisticfree price promotion (75.3%) than when it was offeredwith a sure price promotion (50.0%). Interestingly,no promotion for the Barcelona city hotel (control:53.7%) was not less successful than offering a surepromotion (50.0%).

The difference between the two probabilistic pricepromotions (nonfree, 63.0%, vs. free price, 75.3%) wasonly marginally significant (�2411N = 1625 = 20908,p = 00088), the same as the difference between theprobabilistic nonfree price promotion (63.0%) and thesure price promotion (50.0%; see Table 3). Figure 9displays predictions based on only diminishing sen-sitivity � = 0088 (Tversky and Kahneman 1992) aswell as diminishing sensitivity � = 0088 and Prelec’s(1998) probability weighting function �4p5= exp6−�∗

4− ln p5�7, with � = 1 and � = 0065. As in Experi-ment 3, a suprising observation to make is that ourfindings seem best explained by diminishing sensitiv-ity to prices without weighted probabilities.

Finally, an ANOVA found no significant effect ofour conditions on how much participants liked acity vacation over a beach vacation (mean = 0001,SD = 2071, F 4313225 = 10622, p = 00184; for means and

Table 3 Percentages and Parameter Estimates B for Choice of Barcelona City Hotel over Beach Resort Hotel inExperiment 5a with Sure Price Promotion as Baseline

Nominal logistic regression

Choice ofCondition Barcelona vacation (%) B (SE) �2 p-value 95% CI

Intercept — <− 00001 0000 10000 −00435 004354002215

Sure price promotion 50.0 — — — — —Probabilistic free price promotion 75.3 10115 10080 <00001 00460 10795

403395Probabilistic nonfree price promotion 63.0 00531 2077 00096 −00091 10162

4003195Control (no price promotion) 53.7 00147 0022 00639 −00466 00762

4003135

Notes. The baseline condition is highlighted in grey. Whole model test pseudo-R2 = 00031, N = 326. CI, confidence interval.

Figure 9 (Color online) Predicted Attraction to the 10% ProbabilisticFree and 20% NonFree Price Promotions over the SurePrice Promotion in Experiment 5a

0

1

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1.02.03.04.05.06.07.08.09.0

10.011.012.013.0

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Diminishing sensitivity

Diminishing sensitivity and weighted probabilities

Panel A

Panel B

Note. The exepcted discount was held constant at $20 and the regular priceat $200.

standard deviations by condition, see Table S5 in Sup-plementary Materials and Methods).

Experiment 5b: ResultsAn overall ANOVA revealed a significant differ-ence of condition on number of days booked at the

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Table 4 Means and Parameter Estimates B for Number of Days Booked at the Barcelona City Hotel in Experiment 5b withSure Price Promotion as Baseline

Days Linear regression

Condition Mean (SD) B (SE) t p-value 95% CI

Intercept — 30832 21040 <00001 30480 401844001805

Sure price promotionA 3083 — — — — —410835

Probabilistic FREE price promotionB 4053 00693 2073 00007 00194 10192410975 4002545

Probabilistic nonfree price promotionA 3097 00139 0055 00579 −00355 00634410845 4002515

Control (no price promotion)C 3034 −00495 −1097 <00050 −00989 −00001410545 4002515

Notes. Conditions not connected by the same superscript letter A, B, or C are significantly different (p < 0005), by pairwise student’st-tests. The baseline condition is highlighted in grey. Whole model test R2 = 00053, N = 409.

Barcelona city hotel (F 4314055 = 70515, p < 00001).Table 4 shows the parameter estimates from a lin-ear regression model with number of days bookedat the Barcelona city hotel as the dependent variable,the sure price promotion condition as baseline, andthe remaining three conditions as independent vari-ables (dummy coded with 1 = condition, 0 = notthis condition). As can be seen, participants (N =

409) booked significantly more days at the Barcelonacity hotel when it was offered with a probabilisticfree price promotion (mean = 4053 days, SD = 1097)than when it was offered with a sure price promo-tion (mean = 3083 days, SD = 1083, t44055 = 20731,p = 00007), a probabilistic nonfree price promotion(mean = 3097 days, SD = 1084, t44055 = 20197, p =

00029), or no price promotion (mean = 3034 days, SD =

1054, t44055= 40715, p < 00001). The difference betweenthe probabilistic nonfree price promotion (mean =

3097 days) and the sure price promotion (mean =

3083 days, t44055 = 00555, p = 00579) was not signif-icantly different. Finally, an ANOVA found no sig-nificant effect of our conditions on how much par-ticipants liked a city vacation over a beach vacation(mean = −0019, SD = 2084, F 4314055= 00831, p = 00478;for means and standard deviations by condition, seeTable S5 in Supplementary Materials and Methods).

DiscussionTogether, the results of Experiments 5a and 5b sug-gest that, even for fairly expensive products and in aseparate valuation setting, the probabilistic free pricepromotion can be superior to a sure price promotionof equal expected discount. The findings are particu-larly powerful because they show that the probabilis-tic free price promotion in comparison to the sure pricepromotion may not only encourage more people tomake a planned purchase (i.e., increase the numberof customers) but also the average customer to spend

more money (i.e., increase the average basket size percustomer).12

General DiscussionWhat type of price promotion is more attractive tocustomers: a probabilistic price promotion that offersa chance p to get one’s selected products for free anda chance 41 − p5 to pay the regular, full price or acertain price promotion of equal expected discount?Across four incentive-compatible experiments (Exper-iments 1–4, three in the field and one in the lab-oratory) we considered consumers’ choices betweensure and probabilistic free price promotions (jointvaluation setting) and demonstrated that consumersconsistently, over a range of probabilities (5%–67%),products (candy, DVD rental, rOtring pen), expecteddiscounts, and regular prices ($0.75, $4.50, and $10),preferred the probabilistic free price promotion to thesure price promotion. In addition, extending our find-ings from the joint valuation settings, Experiments 5aand 5b showed, in hypothetical, separate valuationsettings with even more expensive products (hotelrooms; regular price = $200), that the probabilisticfree price promotion can also increase demand for aproduct and do so significantly better than the sureprice promotion in two ways: by attracting more con-sumers (i.e., traffic) and by increasing the averagedemand of consumers (i.e., their basket size). Togetherour experiments demonstrate that a probabilistic freeprice promotion can be a powerful promotions tool toattract more purchases.

12 Note, in this separate valuation setting, the inferiority of the sureprice promotion to the probabilistic free price promotion could alsobe in part a result of the sure discount undermining perceptionsof quality, which free offers are believed less likely to do (see, e.g.,Chandran and Morwitz 2006, Darke and Chung 2005).

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From a theoretical perspective, our findings extendprevious research on psychological pricing by show-ing that they cannot be explained by the uncertaintyor certainty effect. In addition, our results do not seemto be driven by an attraction to zero prices, transac-tion cost aversion, or novelty. Instead, our findingscan be best explained by the assumption that individ-uals behave in a Weber–Fechnerian way: they displaydiminishing sensitivity (�< 1) to the prices.

Limitations and Future ResearchSeveral of our findings are worth further examination.First we did not find any evidence for the uncertaintyeffect (Gneezy et al. 2006, Newman and Mochon 2012,Simonsohn 2009), which would have favored the sureprice promotion. One of the fundamental differenceswe found was that in those uncertainty effect stud-ies where participants were asked to choose betweena sure versus a probabilistic option, the (un)certaintywas in windfall (i.e., there was no cost involved forparticipants) rewards. For example, in Gneezy et al.(2006, Section IV) in one of the choice task condi-tions, participants were asked to choose between asure monetary reward (100 shekels) and a lottery thatwould pay out one of two possible products of differ-ing values (a 50% chance at a 200-shekel gift certifi-cate and a 50% chance at a 400-shekel gift certificatefor a bookstore). Seventy-four percent of their partic-ipants choose the sure 100 shekels in cash, whereasonly 43% of participants did so when the alternativewas a sure 200-shekel gift certificate. By contrast, inour setting, the (un)certainty was in the prices thatconsumers paid in exchange for a good.

Note also that in Dhar and colleagues’ (1995, 1999)research, which we discussed in the section “Pre-vious Consumer Behavior Research on ProbabilisticPromotions,” participants were asked to choose be-tween a sure versus a probabilistic option where the(un)certainty was in the percent discounts that con-sumers would receive when making a payment. Bycontrast, in our setting the (un)certainty was in theabsolute prices that consumers would pay. Dhar et al.(1995, 1999) did not find any difference in the attrac-tion of the sure versus risky option.

Given the differences between our findings, theuncertainty effect findings by Gneezy et al. (2006), andthe findings by Dhar et al. (1995, 1999), one avenuefor future research could be to examine to what extentthe type of focal attribute (e.g., reward, absolute price,or percent discount) and context (e.g., whether thereis a purchase transaction and as such a cost to the con-sumer) influences consumers’ decision-making pro-cess and, ultimately, preferences (i.e., they becomerisk averse, risk seeking, or risk neutral).

The zero price effect is another factor for which wefound no evidence of it being a fundamental driver

of the attraction to the probabilistic free price promo-tion. One possibility is that the excessive attractionto the zero price reported in Shampanier et al. (2007)was not apparent in our probabilistic setup becausethe zero price represents only one of two possibleprice outcomes, and therefore the zero price effectdoes not apply. In the original work on the zero priceeffect, the authors argued that, when there is a zeroprice option that does not have any downside (i.e.,no cost), individuals experience a positive affectivereaction, which acts as a decision-making cue (i.e., thecause of the zero price effect is the affective compo-nent). In the probabilistic free price promotion, how-ever, there is a downside or cost: a chance to pay theregular price. In addition, choosing between a non-free offer and a free offer arguably requires fewercognitive resources than choosing between a nonfreesure offer and a risky offer of two possible outcomes:one free (discounted probabilistic price of $0) and onenonfree (regular price of > $0). This aspect is criticalbecause, in their zero price paper, Shampanier et al.(2007, Experiment 6) showed that making more cog-nitive and deliberate evaluations of alternatives elim-inates the zero price effect because of a lower weighton affective evaluations. Future work could validatethis distinction.

An additional research opportunity may stem fromour surprising findings in Experiments 2, 3, and 5,which suggest that diminishing sensitivity withoutprobability weighting predicts the observed patternof preferences for probabilistic free price promotionsbetter than diminishing sensitivity with probabilityweighting. Future research may want to examine ifand why individuals do not appear to weight proba-bilities in probabilistic price promotions as they havebeen shown to do in simple monetary gambles.

Finally, it remains an open question how robust theattraction of the probabilistic price promotion is todifferent types of framing. For example, in three pric-ing experiments, Yang et al. (2013) found that partic-ipants’ willingness to pay for a risky product (e.g., agift certificate for a Barnes and Noble bookstore thathas a 50% chance to have a $50 value and a 50%chance to have a $100 value) is substantially reducedwhen it is labeled instead as a gamble, lottery, raffle,or coin flip with two outcomes. The authors posit thatthis is due to an aversion to bad deals that causes buy-ers to shift the focus of their attention to risk and theworst possible outcome. In our experiments we didnot present the risky option as a gamble but as a pricepromotion. In addition, our consumers engaged in achoice task typical for purchase situations rather thana pricing task. Future research may want to examineto what extent the bad deal aversion also applies tochoice tasks and thus may reduce the attraction of theprobabilistic free price promotion over the sure pricepromotion when the former is framed in terms of a

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gamble. The question of such potential boundary con-ditions is of great practical importance for marketers.

Supplemental MaterialSupplemental material to this paper is available at http://dx.doi.org/10.1287/mnsc.2015.2328.

AcknowledgmentsThe authors thank their undergraduate research assistantsInsoo Kim and JungEun Lee for collecting data, the inde-pendent video store Hollywood Express in Cambridge,Massachusetts, for allowing the authors to run experimentswith the store’s customers, and Masakazu Ishihara for hishelp with some of the analyses. Finally, the authors are espe-cially indebted to the anonymous reviewers as well as theassociate editor and judgment and decision making depart-ment editor for invaluable guidance and support through-out the process. This research was supported by the Centerfor Advanced Hindsight and a grant awarded to N. Mazarby the Desautels Centre for Integrative Thinking at theRotman School of Management, University of Toronto.

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