Willingness to pay versus expected consumption value in Vickrey auctions for new experience goods.

Very often consumers face a choice between a well-known incumbent brand and a new brand for which they are uncertain about the quality. Learning the quality of the new brand can affect future choices and thereby future payoffs. In this article, we investigate how uncertainty about the quality of a new brand affects the bidding strategy in a Vickrey auction (Vickrey 1961) conducted before a new brand is introduced into the market.

A Vickrey auction is a private value auction in which the bidders submit sealed bids. The winner is the highest bidder and the price equals the second-highest bid. Vickrey (1961) showed that, in such an auction, it is a weakly dominant strategy for people to bid their willingness to pay (WTP) for the good on offer. People have an incentive to truthfully reveal their private preferences because the auction separates what they say from what they pay. Underbidding consumers risk foregoing a profitable purchase, whereas overbidding consumers risk making an unprofitable purchase.

Over the past two decades, the Vickrey auction has been widely used to elicit WTP for food quality attributes (e.g., Alfnes and Rickertsen 2003; Buhr et al. 1993; Fox et al. 1994; Hayes et al. 1995; Hoffman et al. 1993; Lusk, Feldkamp, and Schroeder 2004; Lusk et al. 2004; Melton et al. 1996; Noussair, Robin, and Ruffieux 2004; Roosen et al. 1998; Rousu et al. 2004; Rozan, Stenger, and Willinger 2004; Umberger and Feuz 2004). The appeal of the Vickrey auction for valuation work is that it is demand revealing in theory, relatively simple to explain, and has an endogenous market-clearing price.

Nelson (1970) defined experience goods as products for which the consumption value cannot be fully determined before they are purchased. According to this definition, most food products, including those with search and credence attributes (Darby and Karni 1973), can be considered as experience goods. This is illustrated by Umberger and Feuz (2004) who investigated consumer WTP for beef flavor (an experience attribute), but categorized the beef by its intramuscular fat content (a search attribute) and country of origin (a credence attribute). Consuming a new experience good provides both a consumption value and valuable information that can affect future choices and thereby future payoffs.

Consumers who take part in an experimental auction market where new experience goods are offered might have incentives to bid higher than the expected consumption value to acquire information about how the new good fits into their preference set. Shogren, List, and Hayes (2000) conducted an experiment in which people bid in consecutive auctions over a two-week period to explore what the authors referred to as the "strikingly high price premia paid for new food products in lab valuation exercises" (p. 1016). Their result suggested that preference learning about unfamiliar goods explained the high bids, not the novelty of the lab experience. Furthermore, the bids for unfamiliar goods included an information value that reflected consumers' desire to learn more about the goods.

Whereas Shogren, List, and Hayes (2000) based their analysis on an intuitive argument, this article provides a formal model explaining the high bids for new products as a composite of the expected consumption value of the products and the information value of trying the new product. The remainder of the article proceeds as follows. First, we set up a consumer model with two competing brands, one familiar incumbent brand and a new brand of unknown consumption value. Second, we investigate the consumers' subgame perfect bidding strategy for the two brands in a Vickrey auction that is followed by a multiperiod market. Third, we illustrate the results with numerical examples. Finally, we conclude the article.

The Consumer Model

In response to empirical evidence of an order-of-entry and what he referred to as conventional wisdom in marketing, Schmalensee (1982) developed an economic model to account for the pioneering advantage for experience goods. The model's basic premise is that there is an experiential asymmetry between incumbent and new brands. The consumers have tried and therefore know the consumption value of the incumbent brands. In contrast, the consumers have no experience of the new brands, and are unsure about the consumption value of these brands. This experiential asymmetry creates an advantage for the incumbent brand. See, for example, Kamins, Alpert, and Elliott (2000), Niedrich and Swain (2003), and Villas-Boas (2004) for thorough discussions of the pioneering advantages in the marketing literature.

We extend Schmalensee's (1982) consumer model to include a small-scale Vickrey auction conducted before the introduction of the new brand into the market. We assume that the auction results may affect the auction participants' individual demand, but that the number of participants in the auction is so small that the results have no effect on the aggregated demand or on the producers' pricing policies in later periods. With this in mind, we conduct a partial analysis of the bidding strategies in the Vickrey auction, assuming that the future prices are exogenously given.

Let us consider a narrowly defined product class, such that individual consumers can be sensibly modeled as using, at most, one brand in the class at any instant. It is assumed that the product is what Nelson (1970) called an "experience good," so that the only way consumers can know their own valuation of the good is to purchase and try it. One trial is both necessary and sufficient to determine the consumption value of any single brand. Although the consumers' valuation of the brands and the probability assigned to the new brand being of high consumption value is individual specific, we suppress the individual-specific subscripts throughout the article. The purchase decisions are made using purely private information. (1) We consider two brands of the experience good: one incumbent brand with a well-known consumption value, and a new brand with unknown consumption value.

The market prices of the incumbent and new brands are [p.sub.1] and [p.sub.2], respectively. The consumption value of the incumbent brand is [v.sub.1] and the net consumption value is [v.sub.1] - [p.sub.1]. The consumption value of the new brand is either low or high. If the consumption value of the new brand is low, [v.sub.2L], the net consumption value of the new brand, [v.sub.2L] - [p.sub.2], is lower than the net consumption value of the incumbent brand. If the consumption value of the new brand is high, [v.sub.2H], the net consumption value of the new brand, [v.sub.2]H - [p.sub.2], is higher than the net consumption value of the incumbent brand. (2) The consumers attach a subjective probability of [pi] [member of] (0, 1) to the new brand having a lower net consumption value than the incumbent brand, and a subjective probability of (1 - [pi]) to the new brand having a higher net consumption value than the incumbent brand. (3) The consumption value of the new brand is [v.sub.2L] = [V.sub.2] - a in the case of low quality, and [V.sub.2H] = [[v.sub.2] + a in the case of high quality, so that the difference between the high and low consumption values for the new brand ([v.sub.2H] - [v.sub.2L]) is 2a. We assume that the consumers are risk neutral. The consumption values ([v.sub.1], [v.sub.2L], [V.sub.2H]) and market prices ([p.sub.1], [p.sub.2]) are assumed to be constant over time. We assume that as a result of the individual-specific consumption values, some consumers will prefer to buy the incumbent brand and some will prefer to buy the new brand.

The frequency of purchase is represented by the discount rate in the model. The time between purchases is assumed constant for each consumer and equal to one period, so that the trial of a new brand consumes the entire normal interpurchase time. The one-period discount rate is r [member of] (0, [infinity]). All other factors remaining equal, a more frequent purchase implies a smaller value of r. Given an uncertain end time and a small r, we model the consumers as having infinite horizons.

In any market period, a consumer either knows or does not know the consumption value of the new brand. If the consumer does know the consumption value of the new brand, his or her decision problem is very simple--the consumer simply chooses the alternative with the highest net consumption value. The consumer should choose the new brand if the consumption value of the new brand is high, whereas he or she should choose the incumbent brand if the consumption value of the new brand is low.

If the consumer does not know the consumption value of the new brand, the expected consumption value of the new brand is [pi]([v.sub.2] + a) + (1 - [pi])([v.sub.2] + a) and the expected net consumption value is [pi]([v.sub.2] - a - [p.sub.2]) + (1 - [pi])([v.sub.2] + [p.sub.2]). In a multiperiod market model, it is optimal for the consumer to try the new brand if and only if the expected net current value of trying the new brand and buying the brand with the highest net consumption value from the next period on is higher than the net current value of continuing to purchase the incumbent brand:

(1) [pi]([v.sub.2] - a - [p.sub.2] + ([v.sub.1] - [p.sub.1])/r) + (1 - [pi])([v.sub.2] + a - [p.sub.2])(1 + r)/r > ([v.sub.1] - [p.sub.1])(1 + r)/r.