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.

As the consumption values and prices are constant, and we have an infinite horizon, the maximization problem is the same in all periods. Therefore, if the expected payoff of trying the new brand is negative in the first period, it will also be negative in all later periods. In other words, if the consumer does not try the new brand in the first period he or she will never try it. Assuming an infinite horizon, the sum of the payoffs from the next period on equals the payoff divided by r. (4)

We define the expected payoff of trying the new brand in the market, F([pi], r, a, [p.sub.1], [p.sub.2]), as the expected net current value of trying the new brand, [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, minus the net current value of continuing to purchase the incumbent brand, ([v.sub.1] - [p.sub.1])(1 + r)/r. If F is positive, it is optimal for the consumer to try the new brand in the market. If F is negative, it is optimal for the consumer not to try the new brand in the market.

(2) F([pi], r, a, [p.sub.1], [p.sub.2]) = [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.

Alternatively, F can be expressed as the one-period loss from buying a new brand with a low consumption value instead of the incumbent brand in this market period ([v.sub.2] - a - [p.sub.2] - ([v.sub.1] - [p.sub.1])), multiplied by the probability that the new brand is of low consumption value, [pi], plus the gain from buying a new brand with high consumption value instead of the incumbent brand, from this market period on, ([v.sub.2] + a - [p.sub.2] - ([v.sub.1] - [p.sub.1])) (1 + r)/r, multiplied by the probability that the new brand is of high consumption value (1 - [pi]). (5)

(3) F([pi], r, a, [p.sub.1], [p.sub.2]) = [pi]([v.sub.2] - a - [p.sub.2] - ([v.sub.1] - [p.sub.1])) + (1 - [pi])([v.sub.2] + a - [p.sub.2] - ([v.sub.1] - [p.sub.1]))(1 + r)/r.

We differentiate F with respect to its elements to see if an increase in [pi], r, a, [p.sub.1], and [p.sub.2] increases or decreases the expected payoff of trying the new brand in the market.

(4) [delta]F/[delta][pi] = 2a + ([v.sub.1] - [p.sub.1] - ([v.sub.2] + a - [p.sub.2]))/r < 0

(5) [delta]F/[delta]r = (1 - [pi])([v.sub.1] - [p.sub.1] - ([v.sub.2] + a - [p.sub.2]))/[r.sup.2] < 0

(6) [delta]F/[delta]a = (1 - [pi] + r(1 - 2[pi]))/r

(7) [delta]F/[delta][p.sub.1] = (1 - [pi] + r)/r > 0.

(8) [delta]F/[delta][p.sub.2] = -(1 - [pi] + r)/r < 0.

The expected payoff of trying the new brand in the market is decreasing in [pi] and r, increasing in a for all products that are purchased on a regular basis, increasing in the price of the substitute (the incumbent brand), and decreasing in its own price. An increase in [pi] will decrease the expected payoff from trying the new brand by decreasing the expected consumption value and decreasing the expected information value. A reduction in the purchase frequency, which in this model equals an increase in r, will decrease the value of future payoffs and thereby decrease the expected information value. An increase in a will increase the expected information value, but the effect on the expected consumption value depends on the value of [pi]. If [pi] < 0.5, then an increase in a will have a positive effect on the expected consumption value, whereas if [pi] > 0.5, then an increase in a will have a negative effect on the expected consumption value. The total effect on F of an increase in a is positive for all products that are purchased on a regular basis and that are somewhat likely to be of high consumption value. Remembering that frequent purchase implies a small r, we have, for example, for r = 0.1, that the derivative of F with respect to a is positive if [pi] [less than or equal to] 0.91. The own- and cross-price effects are negative and positive, respectively, as expected.

The Vickrey Auction

If the consumer's first encounter with the new brand is in a Vickrey auction and this encounter is before the introduction of the new brand into the market, the consumer's decision problem is more complicated. For simplicity, let us assume that the auction takes one period, and that the auction participants in that period can buy the products only at the auction. In other words, there are no outside options in the auction period. Furthermore, we assume that the winner of the auction only has to pay the auction price to obtain the product, (6) and that each participant can buy only one product in the auction period. (7) The subgame perfect bidding strategy is to bid so that the consumers maximize the expected net consumption value of the auction and all future market periods, EV.

If the consumer does not obtain any new information about the consumption value in the auction, the consumer still does not know the consumption value of the new brand when he or she encounters it in the market. In that case, the expected net consumption value of all future market purchases in this product class (calculated at the time of the auction) is given by S:

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

If F is positive, it is optimal for the consumer to try the new brand in the market. With a probability of [pi], the new brand has a low consumption value. In that case, the consumer switches back to the incumbent brand in the second market period. With a probability of 1 - [pi], the new brand has a high consumption value. In that case, the testing of the new brand in the first market period leads to a permanent change to the new brand. If F is negative, it is optimal for the consumer not to try the new brand in the market, and to stay with the incumbent brand instead.

For the incumbent brand with a known consumption value, we find the subgame perfect bidding strategy that maximizes the expected net consumption value of the auction and all future market periods by solving the following maximization problem with respect to Bid1:

(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [p.sup.A.sub.1] is the price of the incumbent brand in the auction. If [p.sup.A.sub.1] < Bid1, then the consumer buys the incumbent brand in the auction, otherwise he or she does not. Either way, the consumer gains no new information about the consumption value of the new brand. His or her maximization problem in the next period is unchanged.

For the new brand of unknown consumption value, we find the subgame perfect bidding strategy that maximizes the expected net consumption value of the auction and all future market periods by solving the following maximization problem with respect to Bid2:

(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [p.sup.A.sub.2] is the price of the new brand in the auction, and S, as given in equation (9), is the expected net consumption value from all future market purchases in this product class if no new information is obtained in the auction. If [p.sup.A.sub.2] < Bid2, then the consumer buys the new brand in the auction, otherwise he or she does not. If the consumer buys the new brand, the consumption value of the brand is revealed, and, in the next period, the consumer will choose the alternative with the highest net consumption value. With a probability of [pi], the alternative with the highest net consumption value will be the incumbent brand, and with a probability of (1 - [pi]), the alternative with the highest net consumption value will be the new brand. If the consumer does not buy the new brand in the auction, he or she gains no new information about the consumption value of the new brand, and his or her maximization problem in the market is unchanged.

To find the subgame perfect bidding strategies for the two brands, we use Vickrey's result that, "the optimal strategy for each bidder ... will obviously be to make his bid equal ... to that price at which he would be on the margin of indifference as to whether he obtains the article or not" (Vickrey 1961, p. 20).

We find the subgame perfect bidding strategy for the incumbent brand from equation (10). From Vickrey (1961), we have that when the optimal bid that maximizes equation (10) is equal to the auction price, Bid1 = [p.sup.A.sub.1], the bidders are indifferent about whether they win the auction. This gives us the following equation:

(12) [v.sub.1] - Bid1 + S = S [??] Bid1 = [v.sub.1].

The subgame perfect bidding strategy for the incumbent brand is to bid the consumption value of the brand. The outcome of the auction for the incumbent brand has no effect on what will happen in the market, so S cancels out. The multiperiod solution equals the single-period solution. There is no new information to be gained from consuming the incumbent brand, and, therefore, there is no information value associated with the incumbent brand. In addition, we can see that the subgame perfect bidding strategy for the incumbent brand is independent of [pi], r, a, [p.sub.1], and [p.sub.2].

We find the subgame perfect bidding strategy for the new brand from equation (11). From Vickrey (1961), we have that when the optimal bid that maximizes equation (11) is equal to the auction price, Bid2 = [p.sup.A.sub.2], the bidders are indifferent about whether they win the auction. This gives us the following equation:

(13) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The subgame perfect bidding strategy for the new brand depends on S, and, therefore, on E As F depends on [pi], r, a, [p.sub.1], and [p.sub.2], the subgame perfect bidding strategy for the new brand also depends on [pi], r, a, [p.sub.1], and [p.sub.2].

First, let us assume that the expected payoff of trying the new brand in the market is positive, F > 0, so that the consumer would try the new brand in the first market period. Inserting S = [pi] (([v.sub.2] - a - [p.sub.2])/(1 + r) + ([v.sub.1] - [p.sub.1])/(r(1 + r))) + (1 - [pi])([v.sub.2] + a - [p.sub.2])/r from equation (9) into equation (13) gives us the following subgame perfect bidding strategy for the new brand when F > 0:

(14)

Bid2 = [pi]([v.sub.2] - a) + (1 - [pi])([v.sub.2] + a) + [pi]([v.sub.1] - [p.sub.1] - ([v.sub.2] - a - [p.sub.2]))/(1 + r).

The optimal bid equals the expected consumption value plus the expected information value. In this case, the expected information value is the current value of buying the incumbent brand instead of the new brand if the new brand is of low consumption value, in the next period, ([v.sub.1] - [p.sub.1] - ([v.sub.2] - a - [p.sub.2]))/(1 + r), multiplied by the probability that the new brand is of low consumption value, [pi]. In other words, if the consumer would try the product in the first market period, the expected information value is only associated with the possibility of buying a new brand with a low consumption value in the first market period. (8)

Second, let us assume that the expected payoff of trying the new brand in the market is negative, F < 0. Then, the consumer would stay with the incumbent brand if he or she did not know the consumption value of the new brand. Inserting S = ([v.sub.1]- [p.sub.1])/r from equation (9) into equation (13) gives us the following subgame perfect bidding strategy for the new brand when F < 0:

(15) Bid2 = [pi]([v.sub.2] - a) + (1 - [pi])([v.sub.2] + a) + (1 - [pi])[1)[v.sub.2] + a - [p.sub.2] - ([v.sub.1] - [p.sub.1])]/r.

The optimal bid equals the expected consumption value plus an expected information value. In this case, the expected information value is the value of buying a new brand with a high consumption value instead of the incumbent brand, from the next period on, ([v.sub.2] + a - [p.sub.2] - ([v.sub.1] - [p.sub.1]))/r, multiplied by the probability that the new brand is of high consumption value, (1 - [pi]).

The expected consumption value is the same in equations (14) and (15), [pi]([v.sub.2] - a) + (1 - [pi])([v.sub.2] + a). If F equals zero, the consumer is indifferent as to whether he or she should try the new brand in the market. In that case, we find, by dividing F in equation (3) by (1 + r), that the expected information value in equation (14), [pi]([v.sub.1] - [p.sub.1] - ([v.sub.2] - a - [p.sub.2]))/(1 + r), is equal to the expected information value in equation (15), (1 - [pi])([v.sub.2] + a - [p.sub.2] - ([v.sub.1] - [p.sub.1]))/r. Therefore, if the consumer is indifferent as to whether he or she should try the new brand in the market, the two equations give the same subgame perfect bidding strategy. Hence, as long as r is positive, the subgame perfect bidding strategies for the two brands are continuous functions.

We differentiate the optimal bid functions with respect to [pi], r, a, [p.sub.1], and [p.sub.2] to investigate how the optimal bid for the new brand is affected by changes in the probability of the brand being of low consumption value, the discounting factor, the difference between the high and low consumption value for the new brand, the market price of the incumbent brand, and the market price of the new brand, respectively. Keeping in mind our initial assumptions for [pi], r, a, [p.sub.1], and [p.sub.2], we obtain the following results for a change in [pi]:

(16) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The expected consumption value is decreasing in [pi], whereas the expected information value is increasing in [pi] as long as F is positive. The total effect of an increase in [pi] is a decrease in the optimal bid, independent of the value of F.

Equation (17) shows the effect of a marginal increase in the discounting factor:

(17) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Increasing the discounting factor r is the same as reducing the purchase frequency. This has no effect on the expected consumption value, but it decreases the information value through reducing the current value of future payoffs. An increase in r decreases the optimal bid.

Equation (18) shows the effect of a marginal increase in the difference between the high and low consumption values for the new brand:

(18) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

For products bought very seldom and with very large probabilities of being of low consumption value, the optimal bid decreases as a increases. For other products, the optimal bid increases when a increases. For example, for r = 0.1, the derivative of Bid2 with respect to a is positive if [pi] [less than or equal to] 0.91. The effect of change in a is strongest when F is negative.

Equation (19) shows the effect of a marginal increase in the market price of the incumbent brand:

(19) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The market price of the incumbent brand does not affect the expected consumption value of the new brand, and the total effect of the change in [p.sub.1] is a result of a change in the expected information value. If F is negative, the expected information value and the optimal bid for the new brand increase as the market price of the incumbent brand increases. However, if F is positive, the expected information value and the optimal bid for the new brand decrease as the market price of the incumbent brand increases. The effect of [p.sub.1] on the expected information value occurs through a change in the net consumption value of the incumbent brand, [v.sub.1] - [p.sub.1]. A marginal increase in [v.sub.1] would have had the opposite effect to the marginal increase in [p.sub.1] discussed here.

Equation (20) shows the effect of a marginal increase in the market price of the new brand:

(20) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The expected future market price of the new brand does not affect the expected consumption value of the new brand, and the effect of the change in [p.sub.2] is a change in the expected information value. If F is negative, the expected information value and the optimal bid for the new brand decrease as the market price of the new brand increases. However, if F is positive, the expected information value and the optimal bid for the new brand increase as the market price of the new brand increases.

Numerical Examples

To illustrate how the optimal bid for the new brand changes with [pi], r, a, [p.sub.1], and [p.sub.2], we present four figures. In all four figures, [pi] varies from 0 to 1, and one of the other variables takes several values. The basic model included in all four figures is [v.sub.1] = 1.0, [v.sub.2] = 0.8, [p.sub.1] = 0.6, [p.sub.2] = 0.4, r = 0.1, and a = 0.2.

There are two things that we can see from all four figures (figures 1-4). First, we can see that an increase in [pi] decreases the optimal bid. However, the expected information value, here seen as the difference between the optimal bid and the expected consumption value, increases when [pi] increases as long as [pi] is not so large that F becomes negative. This is consistent with equation (16). Second, we can see that the expected information value is largest for those consumers who are indifferent as to whether they will try the new product, F = 0.

Figure 1 illustrates how an increase in r from 0.1 to 0.2 and then to 0.3 affects the optimal bid. We can see that an increase in the discounting factor r decreases the optimal bid. Increasing r has no effect on the expected consumption value, but it decreases the information value by reducing the current value of future payoffs. This is consistent with equation (17).

Figure 2 illustrates how a change in a from 0.2 to 0.3 affects the optimal bid. When a equals 0.2, then [v.sup.2L] = 0.6 and [v.sup.2H] = 1.0, and when a equals 0.3, then [v.sub.2L] = 0.5 and [v.sub.2H] = 1.1. We can see that an increase in a increases the slope of the expected consumption value curve. Furthermore, an increase in a increases the expected information value. In other words, when a increases, the difference between the optimal bid and the expected consumption value increases. These results are consistent with equation (18).

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

Figure 3 illustrates how a change in [p.sub.1] from 0.5 to 0.6 and then to 0.7 affects the optimal bid. We can see that an increase in [p.sub.1] increases the optimal bid if F is positive. However, if F is negative, the optimal bid decreases when [p.sub.1] increases. These results are consistent with equation (19).

Figure 4 illustrates how a change in [p.sub.2] from 0.4 to 0.3 and then to 0.5 affects the optimal bid. We can see that an increase in [p.sub.2] decreases the optimal bid if F is negative. However, if F is positive, the optimal bid decreases when the consumption value of the incumbent brand increases. If [p.sub.2] had been increased to 0.6, there would have been no expected information value and the optimal bid curve would have been equal to the expected consumption value curve. These results are consistent with equation (20).

Concluding Remarks

In Vickrey auctions for a new experience good, it is optimal for consumers to bid higher than the expected consumption value to obtain information about how the new good fits into their preference set. The degree of uncertainty about the consumption value, the purchasing frequency, and expected future market prices all affect the value of the quality information and thereby the consumers' WTP for the new brand.

The subgame perfect bidding strategy discussed in this article is consistent with Vickrey's (1961) optimal bidding results. However, a part of the WTP is based on a potential surplus that can be gained in future periods. It is also important to notice that the information value is equally important in other incentive-compatible methods for eliciting WTP for products with unknown consumption values.

The predictions of the model are consistent with the experimental results in Shogren, List, and Hayes (2000), who explored what they referred to as the strikingly high price premia paid for new food products in lab valuation exercises. They found that the WTP for familiar goods was unaffected by trying the good, whereas the WTP for unfamiliar goods was reduced after the consumers had tried them. The reduction in WTP after the consumers had tried the unfamiliar good can be interpreted as a reduction in the information value from further testing of the good.

Researchers cannot affect the valuation of the incumbent brands, the expected future market prices, or the purchasing frequency, but they can significantly reduce the uncertainty about the consumption value of the new brand. If the consumers know the consumption value with certainty, the subgame perfect bidding strategy is to bid the expected consumption value of the new good. Therefore, if the uncertainty about the consumption value is not an important part of an experimental market study, it might be wise to allow the consumers to test the product before the market experiment. This will reduce the uncertainty about the consumption value and thereby reduce the importance of elements outside of the experiment, such as the expected future market prices, or the purchasing frequency.

Last, it is worth noting that the auction differs significantly from ordinary markets in that it is a weakly dominant strategy for all consumers to bid their WTP for the new brand; this is the case even for those who would not try the new brand in the market because the market price is higher than their WTP.

[Received May 2005; accepted January 2007.]

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(1) A reason can be that unobservable private taste variations make other consumers an ineffective source of value information. The large number of products in some product categories is clear evidence that consumers do not agree on which brands give the highest value.

(2) These restrictions are consistent with Schmalensee (1982), although he assumed that [v.sub.2L] < [v.sub.2H] = [V.sub.1] and used optimizing firms to find [p.sub.2] < [p.sub.1].

(3) In a product category where there are many alternatives, as, for example, breakfast cereals, the incumbent brand can be interpreted as the preferred choice before the new brand is introduced. The more alternatives the consumer can choose from, the lower is the probability that the new brand will have a higher net consumption value than the brand that is the preferred brand before the new brand is introduced.

(4) For more information on the discounting, see Alfnes (2007).

(5) See Alfnes (2007) for the derivation of equations (3).

(6) Some papers, such as Hayes et al. (1995) and Shogren, List, and Hayes (2000), used a Vickrey auction to elicit the WTP to exchange an endowed base product for another product. In that case, the winner has to give up both the endowed base product and pay the auction price. See Corrigan and Rousu (2006) for an investigation of the effect of endowing the participants with a base product.

(7) To guarantee that the participants do not buy more than one product, random drawing of a binding product and/or trial is commonly used in auction experiments where the consumers bid on more than one product and/or bid on the same products in repeated trials.

(8) It is often the case that the new brand will not be available in the first market period after the auction. If the new brand enters the market in market period n, then the benefit of the quality information comes n - 1 periods later, and the information values in equations (14) and (15) must be divided by [(1 + r).sup.n - 1]. If the product never enters the market, then we can model that as n = [infinity]. This gives us an information value that is equal to zero.

Frode Alfnes is associate professor, Department of Economics and Resource Management, Norwegian University of Life Sciences. He was a visiting scientist at Iowa State University when parts of this article were written.

Financial support for this research was provided by The Research Council of Norway, grant no. 159523/110.