The Effect of Offer Verifiability on the Relationship 

Between Auctions and Multilateral Negotiations*

Charles J. Thomas Bart J. Wilson

Federal Trade Commission Interdisciplinary Center for Economic Science

Division of Economic Policy Analysis George Mason University

600 Pennsylvania Ave., NW 4400 University Drive, MSN 1B2 

Washington, D.C. 20580 Fairfax, VA 22030

E-mail: cjthomas@ftc.gov E-mail: bwilson3@gmu.edu

November 2001 

Abstract: We use the experimental method to compare second-price auctions to “verifiable” 

multilateral negotiations in which the sole buyer can credibly reveal to sellers the best price offer 

it currently holds. We find that transaction prices are lower in verifiable multilateral negotiations 

than in second-price auctions, despite the two institutions’ seeming equivalence. The difference 

occurs because low-cost sellers in the negotiations tend to submit initial offers that are less than 

the second-lowest cost. We also compare the two institutions to previously studied first-price 

auctions and multilateral negotiations with nonverifiable offers. Second-price auctions yield the 

highest prices, followed in order by verifiable negotiations, nonverifiable negotiations, and firstprice auctions. 

 

*

 We thank Paul Oyer, David Schmidt, and seminar participants at George Washington University and the 

INFORMS 2001 Annual Meeting for helpful comments, the International Foundation for Research in Experimental 

Economics for providing financial support, and Todd Swarthout for writing the software. The data and a 

demonstration copy of the instructions are available upon request. This work reflects the opinions of the authors and 

does not necessarily reflect the position of the Federal Trade Commission or any individual Commissioner. 

JEL: C78, D44, C9, L14

Keywords: multilateral negotiations, bargaining, auctions, e-commerce 
1

1. Introduction

One of the more interesting facets of voluntary exchange is how changes in the strategic 

environment lead to differences in transaction outcomes. For example, increasing the value of a 

player’s threat-point payoff increases their payoff from Nash bargaining. The theoretical work in 

Holt [1980] shows that switching from first-price auction rules to second-price auction rules 

decreases the auctioneer’s expected payoff if bidders are risk averse. Finally, comparing the 

pioneering experimental work in Chamberlin [1948] and Smith [1962] illustrates that changing 

the nature of the information available to the players can dramatically influence the price and 

efficiency of an exchange process. With this insight in mind, in this paper we use the 

experimental method to examine and compare four exchange mechanisms in a procurement 

setting in which a buyer faces several sellers that have privately known production costs. 

The first two institutions are variants of the multilateral negotiations introduced in 

Thomas and Wilson [2001]. In this common exchange mechanism, a buyer solicits price offers 

from multiple sellers, and then it elicits more favorable offers by playing the sellers off one 

another until it accepts one of the offers or breaks off the negotiations. Among other settings, 

multilateral negotiations are pervasive in industrial procurement, the securing of high-end job 

offers, and the purchasing of expensive goods such as computers, contractors’ services, and 

automobiles. 

The second two institutions are the first-price auction and the second-price auction. 

These well-known auction formats and their theoretically isomorphic variants, the Dutch auction 

and the English auction, are used extensively to allocate products as varied as flowers, art, 

produce, fish, government securities, and offshore mineral rights.1

 More recently, several 

governments have used auctions to allocate such valuable resources as radio spectra, electric 

power, and pollution rights.2

 

We hypothesize that the outcome of a multilateral negotiation is critically influenced by 

the buyer’s ability to credibly reveal to a seller the price offers it holds from other sellers. With 

that hypothesis in mind, in Thomas and Wilson [2001] we investigated nonverifiable multilateral 

negotiations, in which the buyer cannot credibly reveal the best offer it currently holds. In many 

negotiation settings it is reasonable to assume that the buyer is unable or unwilling to credibly 

 

1

 See Milgrom and Weber [1982] and McAfee and McMillan [1987]. 

2

 See McAfee and McMillan [1996], Wolfram [1998], and Cason [1995] for details, respectively. 
2

reveal rival sellers’ offers. We compared nonverifiable negotiations to first-price auctions, 

because the two institutions appeared to be conceptually similar. We found that the two 

institutions’ prices are indistinguishable with four sellers, but that negotiated prices exceed 

auction prices with two sellers. 

In this paper we investigate verifiable multilateral negotiations, in which the buyer can 

credibly reveal the best offer it currently holds. Internet-based third-party business-to-business 

exchanges provide one of the best examples of institutions in which a buyer could credibly 

reveal its best offer. As an independent third party with a reputation to maintain and legal 

responsibilities to uphold, a business-to-business exchange can credibly authenticate the best 

offer that a buyer currently holds. Even though most people likely view auctions as the 

dominant exchange mechanism in B2B commerce, negotiations are becoming more common on 

B2B sites. For example, at www.chemconnect.com, a purchasing manager can invite its 

suppliers into a “Corporate Trading Room” to settle on a transaction for raw chemical materials.3 

We compare verifiable negotiations to second-price auctions because, as we will argue, the two 

institutions appear to be conceptually similar. Moreover, examining these two institutions 

naturally complements our earlier work. 

In addition to comparing the outcomes of verifiable multilateral negotiations and secondprice auctions, we integrate those results with the results of our earlier experiment that compared 

nonverifiable multilateral negotiations and first-price auctions. The integrated results provide a 

detailed picture of the relationships among the four institutions. 

 The outcomes of multilateral negotiations are not only interesting in their own right. 

Their relationship to the outcomes of various auction formats is interesting because of its 

implications for institutional design. The fact that some buyers in an industry use multilateral 

negotiations, while others use one-shot sealed-bid auctions, suggests either that the processes are 

outcome-equivalent or that there are factors that make one process more favorable than the other. 

Identifying these factors should lead to a more informed selection of an exchange process. 

We study the relationship between second-price auctions and verifiable multilateral 

negotiations by permitting fairly unstructured negotiation between a buyer and several sellers. 

Each experimental session anonymously matches a buyer with either two or four sellers, and 

 

3

 The World Chemical Exchange at www.chemconnect.com reports that it in first quarter of 2001, more than $2 

billion worth of transactions were conducted at its site. 
3

consists of several periods of negotiations and second-price auctions. When multilateral 

negotiations are employed, the buyer can communicate electronically in real-time with the 

sellers, but the sellers cannot communicate with each other. When auctions are employed, the 

buyer plays a passive role, and none of the players can communicate with each other. We match 

sellers’ costs across sessions and institutions to study whether outcomes depend on which 

institution is used. Similarly, we vary the number of sellers to see how the outcomes change 

within an institution. 

We find that transaction prices are strictly lower in verifiable multilateral negotiations 

than in second-price auctions, despite the two institutions’ seeming equivalence. Price-setting in 

the second-price auctions largely reflects the sellers’ dominant strategy, and the across-institution 

price difference emerges when there is a large spread between the lowest and second-lowest 

costs. In those cases the low-cost seller’s initial offer in the negotiations tends to be below the 

second-lowest cost, eliminating the need for further negotiation. When the cost spread is small, 

the two institutions’ prices are statistically indistinguishable and are approximately equal to the 

second-lowest cost. Using the results of our earlier study, we also compare the two institutions 

with first-price auctions and with nonverifiable multilateral negotiations. All four institutions are 

highly efficient, with second-price auctions yielding the highest prices, followed in order by 

verifiable negotiations, nonverifiable negotiations, and first-price auctions. 

The paper is structured as follows. Section 2 describes the framework we envision 

underlying both the auction and the negotiation settings, and it explains the reasoning behind our 

hypothesis that the outcomes of second-price auctions and multilateral negotiations should be 

identical. Section 3 describes the experimental design and the procedures we use to examine the 

relationship between the two institutions. Sections 4 and 5 present our within-experiment and 

across-experiment results, respectively, while Section 6 briefly concludes. 

2. Related Theoretical Background 

While auctions have been studied extensively, multilateral negotiations have not been 

formally modeled in the bargaining literature, presumably due to their strategic complexity. 

Hence, our study is based upon our intuition about how second-price auctions and verifiable 

multilateral negotiations should be related. We explain that intuition below, but first we describe 
4

second-price auction theory and our conception of how verifiable multilateral negotiations are 

executed. 

Consider a setting in which T risk-neutral sellers compete to fulfill a contract for a single 

risk-neutral buyer. VB is the commonly known value that the buyer places on having the contract 

fulfilled. Each seller’s cost c is a privately known independent draw from the continuous 

distribution function G with density g that is strictly positive over the support [c,c ]. In the 

auction literature, this is referred to as a symmetric independent private value (IPV) setting. 

The second-price auction proceeds with each seller simultaneously submitting a secret 

price offer. The seller offering the lowest price is awarded the contract at the lesser of the next 

highest price offered and VB, provided the lowest price is less than VB. All other sellers receive 

nothing. The winning seller’s profit is p – cw, where p is the transaction price and cw is the 

winning seller’s cost. The buyer’s profit is VB – p, total surplus is VB – cw, and efficiency is (VB – 

cw)/( VB – c1), where c1 is the lowest realized cost. Each seller’s unique dominant strategy is to 

offer a price equal to its cost. 

The multilateral negotiation proceeds with each seller simultaneously making a secret 

price offer to the buyer in the first period of play. The buyer can accept one of the offers or 

reject them all. If the buyer accepts an offer, then the game concludes and the transaction price 

is the price p offered by the winning seller. As in the auction setting, the winning seller’s profit 

is p – cw, where cw is the winning seller’s cost, and the buyer’s profit is VB – p. If the buyer 

rejects all offers, then the buyer simultaneously announces to each seller the best standing offer it 

possesses.4 The sellers can respond to this communication by making additional price offers, the 

buyer can accept or reject these new offers, and so on. The game continues in this fashion until a 

transaction occurs. 

Within the auction literature, it has been hypothesized that multilateral negotiations bear 

some relation to second-price or English auctions (e.g., see Waehrer and Perry [1999]). The 

general argument is that the buyer should be able to obtain concessions from a seller until the 

seller’s offer is just equal to the seller’s cost, with the implicit assumption that the negotiations 

conclude when only a single seller remains. We agree in part with this conjecture, but our 

intuition is that the relationship between multilateral negotiations and various auction formats 

 

4

 As an alternative formulation, one could consider a setting in which the buyer can credibly reveal rivals’ offers, but 

must inform the sellers individually rather than simultaneously. 
5

depends critically on the buyer’s ability to credibly reveal to a seller its rivals’ offers. 

Specifically, if the offers can be credibly revealed, then the multilateral negotiation should be 

similar to a second-price or English auction, because sellers should be willing to make 

concessions until the price reaches their cost. If the offers cannot be credibly revealed, then the 

multilateral negotiation should be similar to a first-price auction. 

To understand why the ability to credibly reveal offers might play a crucial role, consider 

the problem facing a seller in a multilateral negotiation when its rivals’ offers cannot be credibly 

revealed. When the buyer tries to use a rival’s offer to elicit a better offer from the seller, the 

seller must be concerned that the buyer is not being truthful about the terms or the existence of 

the rival’s offer. Consequently, the seller must be aware of the danger that he could end up 

bidding against himself by offering price reductions that are undercut by fictitious discounts 

from a rival. This danger is not present when the best offer can be credibly revealed. 

For several reasons, the preceding relationships may not be exact, either empirically or 

theoretically. First, in practice the outcomes of multilateral negotiations likely depend critically 

on the players’ ability to haggle. For example, once the buyer determines which seller has the 

lowest cost in a verifiable multilateral negotiation, the buyer and that seller still may negotiate 

over the division of the remaining surplus. To the extent that the buyer is able to extract further 

concessions from the low-cost seller once the price has reached the second-lowest cost, then the 

negotiated price will be lower than the price in the second-price auction.

Second, in multilateral negotiations there must be incentives for sellers to make serious 

offers. That is, there is no reason for sellers to make an offer until the last possible moment, 

particularly if there are no delay costs5

 and if they are concerned that serious initial offers either 

will be used against them by the buyer later in the negotiation, or will provoke a sequence of 

aggressive price cuts.6

 This effect would tend to make negotiated prices exceed second-price 

auction prices. In our experimental framework, there exists a time limit on each negotiation 

period, and there clearly exist frictions that prevent the buyer from receiving infinitely many 

offers. Consequently, there are delay costs, and a seller might be concerned that it will be left 

 

5

 Regardless of the verifiability of offers, a multilateral negotiation will be equivalent to a first-price auction if the 

buyer’s cost of obtaining additional offers exceeds the maximum possible gain from obtaining those offers, or if the 

discount factor is zero (so that future transactions have no value). In both cases the buyer will accept one of the 

initial offers. 

6

 Roth and Ockenfels [2001] provide evidence to suggest that concerns of this nature lead to last-minute bidding, or 

“sniping,” in online auctions with a fixed ending time. 
6

out of the communication process if it does not make serious offers. These market frictions 

would tend to reduce negotiated prices, but not necessarily to a level below that of second-price 

auction prices. 

3. Experimental Design and Procedures 

Using “S” to denote a sequence of second-price auctions and “V” to denote a sequence of 

verifiable multilateral negotiations, we pair two treatments, one with the sequence VSSV, and one 

with the sequence SSVS. The first and third sequences consist of 12 transactions; the second 

consists of 16, while the fourth consists of 6.7 Later we refer to each of the four sequences as a 

“regime.” We vary these two treatments by changing the number of sellers. One has two sellers 

per buyer, while the other has four sellers per buyer. 

For each of the four treatments, {2 sellers, 4 sellers} × {VSSV, SSVS}, we have four 

groups of subjects. Each subject is assigned a specific role in a specific group for the duration of 

the experiment. A seller’s characteristics consist of 46 random cost draws from the Uniform 

distribution on the support [0.00, 6.00], one for each time period. Of the eight groups with four 

sellers, seller i (i = 1, 2, 3, 4) has the same cost draws across groups. Of the eight groups with 

two sellers, seller i (i = 1, 2) has the same cost draws across groups. Moreover, the costs of 

sellers 1 and 2 in the two-seller treatment are the same as the costs of sellers 1 and 2 in the fourseller treatment.

Our experiment consisted of a total of 736 second-price auctions or rounds of verifiable 

multilateral negotiations using 64 undergraduate student volunteers (48 sellers and 16 buyers).

Some students had participated previously in market experiments, but with substantially different 

trading institutions. No subject participated in more than one of the sessions. 

In addition to reading self-paced instructions displayed by the software, the subjects 

followed along as the experiment monitor read aloud from a handout with both additional and 

review information.8

 The public instructions explained (and made common knowledge) that the 

sellers’ costs were assigned randomly each period and that the distribution of the draws was 

 

7

 We employ these sequences, rather than the more common SVS and VSV sequences of treatments, to permit 

comparisons with the experimental results regarding first-price auctions and nonverifiable multilateral negotiations 

in Thomas and Wilson [2001]. The experiment reported in that paper used such sequences to get a sufficient 

number of auction observations while satisfying a time constraint on the experiment’s length. 
7

U[0.00, 6.00]. The instructions also revealed that the buyer’s value was 6.00. Revealing the 

buyer’s value is consistent with prior buying auction experiments in which bids are constrained 

to be nonnegative, which effectively bounds the buyers’ bids between zero and their respective 

values. Here, we effectively bound the sellers’ price offers between their respective costs and 

6.00. 

The random cost draw for a given period was disclosed to the subject at the beginning of 

the period. In the second-price auction environment, after learning his cost each seller had four 

minutes to submit his private offer to sell, though this limit was never binding. The computer 

automatically awarded the sale to the seller that submitted the lowest offer once all of the offers 

had been submitted, provided that the lowest offer was less than 6.00. The winning seller was 

paid the lower of the second-lowest price and the buyer’s value. At the end of the auction, the 

final market price was announced electronically to all market participants, after which the 

session proceeded to the next period. 

In the verifiable multilateral negotiation environment, after learning his cost each seller 

had 30 seconds in the first phase of the period to submit his initial offer to the buyer. The 

instructions indicated that the seller would be able to lower his offer at any time in the second 

phase of the period by submitting a new binding offer. Once the buyer received all initial offers, 

the clock was reset to four minutes for the negotiation phase. At any time during the negotiation 

phase, a seller could (only) lower his offer, and the buyer could accept the offer of a single seller. 

Furthermore, a buyer and a specific seller could use text messaging over the computer network to 

engage in nonbinding discussions concerning a transaction. The buyer could negotiate 

individually with any seller, but only one at a time, while retaining standing offers from the other 

sellers. In contrast, sellers could only communicate with their buyer. A transcript of the 

discussions between the buyer and the seller remained on the screen for the duration of the 

period. The subjects only knew the laboratory identification number of the parties with whom 

they were communicating. Once the buyer accepted an offer, the final market price was 

announced electronically to all market participants,9

 after which the session proceeded to the 

 8

 The instructions for the second-price auctions are based upon those used by Cox, Roberson, and Smith [1982] and 

Cox, Smith, and Walker [1983, 1988]. The instructions for the multilateral negotiations are newly developed, but 

follow those for the second-price auctions to the extent possible. 

9

 There were only two cases in which the buyer did not accept any offer. Both of these were in the two-seller 

treatment when the costs of both sellers were relatively close to 6.00.
8

next period. At all times, the best submitted offer was visible to all participants, and they all 

were informed in the instructions that this was the case. 

The subjects were not told the number of trading periods in the session or in any 

institutional regime within the session. Moreover, the subjects did not know the nature of any 

future trading institution, as the instructions for an institution were displayed only prior to 

commencing trade. It was public information that the same set of sellers was matched with the 

same buyer for the duration of the experiment. Such repeated play is a common feature of 

naturally occurring markets and previous auction experiments.10 

Participants received $5 for showing up on time, plus their salient earnings. In the fourseller sessions, the buyers’ exchange rate was US$1 for 7 experimental dollars, and the sellers’ 

exchange rate was US$1.50 for 1 experimental dollar. In the two-seller sessions, the exchange 

amounts were 4 and 2 experimental dollars for each US$1, respectively. To equalize the buyers’ 

and sellers’ earnings expectations, the exchange rates are more favorable to the sellers because a 

buyer receives a payoff every period, but a seller only expects to win every two or four periods. 

Based upon the theoretical second-price auction outcomes for the observed cost draws, these 

exchange rates reflect an average cash payoff of $21.50 for all types of agents. In addition to the 

$5 fee for showing up on time, the average subject’s earnings for this experiment were $20.50. 

The average session lasted 75 to 90 minutes. 

4. Within-Experiment Results

For each period of play, our data set includes the transaction price, each seller’s cost, 

each seller’s initial and subsequent offers in the multilateral negotiations, and a verbatim record 

of the communications between buyers and sellers. The latter is not part of our statistical 

analysis, but it provides qualitative insights about the players’ strategies and their beliefs about 

other’s strategies. The data permit us to compare the transaction prices and efficiency for the 

different institutions and numbers of sellers, a summary of which is in Table 1. 

We present our within-experiment results as a series of three findings. Our qualitative 

results are displayed in tables and figures, and our quantitative results are derived by analyzing 

 

10 For example, see Coppinger, Smith and Titus [1980], Cox, Roberson, and Smith [1982], Cox, Smith, and Walker 

[1983], and Kagel, Harstad, and Levin [1987]. 
9

the data using a linear mixed-effects model for repeated measures.11 Table 2 reports the model’s 

regression results for each of the four regimes. The dependent variable is the observed 

transaction price. The treatment effects (Two vs. Four Sellers, and Verifiable Negotiation vs. 

Second-Price Auction) and an interaction effect from the 2 × 2 design are modeled as (zero-one) 

fixed effects, while the 16 independent sessions are modeled as random effects, ei. Specifically, 

we estimate the model 

ij i Twoi Verifiablei Twoi Verifiablei ij Price = μ + e + β + β + β × + ε 1 2 3 , 

where ) ~ (0, 2 N σ 1 ei and ~ (0, ) 2

ij N σ 2,i ε . The sessions are indexed by i and the repeated periods 

are indexed by j (e.g., j = 1, 2, ..., 12, for the first regime of twelve periods).12 We accommodate 

heteroskedastic errors by session when estimating the model via maximum likelihood.

 Estimates of the treatment effects are easy to compute with this specification. The 

intercept μ is the expected price in a four-seller second-price auction, μ + β1 is the expected price 

in a two-seller second-price auction, μ + β2 is the expected price in a four-seller verifiable 

multilateral negotiation, and μ + β1 + β2 + β3 is the expected price in a two-seller verifiable 

multilateral negotiation. Across-treatment price differences, and differences-in-differences, also 

are easy to compute. 

Our first finding is a baseline result that establishes that the change in the number of 

sellers affects transaction prices in the manner predicted by standard oligopoly models. 

Finding 1: For all regimes and institutions, reducing the number of sellers from four to two 

significantly increases transaction prices. 

Evidence: Table 1 reports the average transaction price for the first 12 periods, by institutional 

regime and by the number of sellers. The average price in the second-price auctions is 3.03 with 

four sellers and is 4.17 with two sellers, which is a 37.6% increase. The average price in the 

multilateral negotiations is 2.50 with four sellers and is 3.46 with two sellers, which is a 27.7% 

increase. Similar price comparisons can be made for the remaining periods. The results in both 

institutions suggest that the transaction price increases as the number of sellers decreases. 

 

11 See Laird and Ware [1982] and Longford [1993] for a description of this technique commonly employed in 

experimental sciences. 

12The linear mixed-effects model for repeated measures treats each session as one degree of freedom with respect to 

the treatments. Hence, with four parameters, there are 12 degrees of freedom for the estimates of the treatment fixed 

effects (16 sessions – 4 parameters). 
10

Figure 1(a) displays by treatment the transaction prices in each of the first twelve periods, 

averaged over the four sessions in each treatment. Figures 1(b) through 1(d) display the same 

information for the remaining three regimes. As with the data presented in Table 1, visual 

examination of the average prices in the two-seller and four-seller SSVS treatments suggests that 

in each period the transaction prices are higher with fewer sellers. The same conclusion holds 

for the VSSV treatments. 

The estimates in Table 2 from the linear mixed-effects model for repeated measures 

provide a formal test of this finding. The coefficient on the Two dummy variable, which 

measures the primary effect of the two-seller treatment, is positive and highly significant in all 

four regimes, raising transaction prices by 1

ˆ

β = 1.13, 1.61, 0.82, and 2.26 experimental dollars, 

respectively (p-value = 0.0013, 0.0000, 0.0191, and 0.0000). Because the coefficient 3 β

ˆ on the 

interaction term is insignificant in each regime, we cannot reject the null hypothesis that the price 

change induced by reducing the number of sellers is the same across institutions.

We now turn our attention to our primary findings that compare the transaction prices and 

the efficiency of second-price auctions and verifiable multilateral negotiations. 

Finding 2: For all regimes with paired auctions and negotiations, verifiable multilateral 

negotiation prices are statistically lower than second-price auction prices with both two and four 

sellers. The magnitude of the across-institution price difference is invariant to the number of 

sellers. 

Evidence: Table 1 reports that in Regime 1, with four sellers, the average price is 3.03 in the 

second-price auctions and is 2.50 in the verifiable multilateral negotiations. With two sellers, the 

average price is 4.17 in the second-price auctions and is 3.46 in the verifiable multilateral 

negotiations. Price comparisons in Regimes 3 and 4 yield similar conclusions. 

Reference to Figure 1, but now comparing the average prices across sequences for a fixed 

number of sellers, illustrates the across-institution differences per period. The price patterns in 

the four-seller treatments are noticeably different, as are the price patterns in the two-seller 

treatments. 

The estimates in Table 2 provide a formal test of this finding. As we indicated earlier, 

the estimate of the Verifiable coefficient, 2

ˆ

β , represents the difference between the expected 
11

prices of the multilateral negotiations and the second-price auctions, holding the number of 

sellers constant at four. The point estimates for Regimes 1, 3, and 4 are –0.59, –1.62, and –0.73, 

respectively, and are statistically significant (p-values = 0.0402, 0.0005, and 0.0276), so we 

reject the null hypothesis in favor of the alternative that verifiable prices are less than secondprice auction prices. This is not too surprising, given our visual examination of the four-seller 

transaction prices in Table 1 and Figure 1. With four sellers in second-price auctions, the 

estimated transaction prices are given by μˆ , so the Verifiable treatment lowers four-seller 

transaction prices by 19%, 50%, and 27% to 2

ˆ μˆ + β = 2.49, 1.59, and 1.94. 

For two sellers the total effect of the Verifiable treatment significantly lowers transaction 

prices in Regimes 1, 3, and 4 by 2 + 3 = ˆ ˆ β β –0.70, –1.56, and –1.40 experimental dollars, 

respectively, below the level for two sellers in second-price auctions (p-values = 0.0319, 0.0016, 

and 0.0012). Because the coefficient 3 β

ˆ on the interaction term is insignificantly different from 

zero, we cannot reject the null hypothesis that the across-treatment magnitudes do not change 

with the number of sellers. With two sellers in second-price auctions, the estimated transaction 

prices are given by 1

ˆ μˆ + β , so the Verifiable treatment lowers two-seller transaction prices by 

17%, 39%, and 28% to + 1 + 2 + 3 = ˆ ˆ ˆ μˆ β β β 3.50, 2.473, and 3.53.

 It is worth noting that verifiable negotiation prices are always lower than second-price 

auction prices, regardless of the sequencing of the institutions. This robustness to the ordering 

makes more compelling our inference from Finding 2 that the observed effects are due to the 

institutional treatment rather than to unidentifiable factors or sampling variation. 

Despite the robustness of the price ranking of the verifiable negotiations and the secondprice auctions, there is some weak evidence of a hysteresis or learning effect in Regime 2, which 

matches second-price auctions across the two sequence treatments. Those sessions that use 

verifiable multilateral negotiations in Regime 1 have somewhat higher second-price auction 

prices, 2

ˆ

β = 0.41 (p-value = 0.0898), as perhaps the sellers learn to play their dominant strategy. 

However, in Regime 3 those same sellers nearly play according to the dominant strategy for a 

second-price auction. 

 
12

Finding 3: For all regimes and institutions, the level of efficiency is not significantly affected by 

any primary or interaction effects, with one exception. There is weak evidence in Regime 1 that 

the primary effect of changing from auctions to multilateral negotiations slightly decreases the 

level of efficiency. 

Evidence: Table 1 reports the average efficiency by institutional regime and by the number of 

sellers. The observed high efficiency levels are consistent with those reported in previous 

auction experiments.13 Table 3 reports the results from a linear mixed-effects model with the 

efficiency level as the dependent variable. As in our pricing analysis, the baseline treatment is 

four sellers in second-price auctions. In the auction treatment, reducing the number of sellers 

from four to two has no effect on efficiency, as the coefficient 1 γˆ is insignificant for Regimes 1 

through 4 (p-values = 0.7697, 0.3479, 0.8432 and 0.9950). The coefficient 3 γˆ on the interaction 

term Two × Verifiable is also insignificant in all four regimes (p-values = 0.3702, 0.4539, 0.6764 

and 0.7236). Thus, in the negotiation treatment, reducing the number of sellers from four to two 

has no effect on efficiency. In Regime 1 we can reject the null hypothesis at a level of 0.0764 

that efficiency in the four-seller negotiations equals efficiency in the four-seller second-price 

auctions in favor of the alternative that efficiency in the four-seller negotiations is lower ( 2 γˆ = –

3.93), but we fail to reject the null in Regimes 3 and 4 ( 2 γˆ =–2.00 and –3.64, and p-value = 

0.5170 and 0.2923). 

Findings 2 and 3 report that transaction prices with both two and four sellers are strictly 

lower in verifiable multilateral negotiations than in second-price auctions, but that efficiency is 

almost always the same. From these two findings we infer that switching from verifiable 

multilateral negotiations to second-price auctions transfers surplus from the buyer to the most 

efficient seller. This suggests that the buyer should prefer employing verifiable multilateral 

negotiations to second-price auctions. 

In Section 2 we offer possible reasons why the outcomes of auctions and negotiations 

might differ. Examination of the data reveals that negotiation prices are less than second-price 

auction prices, but not for the reasons we hypothesized ex ante. Figure 2 plots every period’s 

average transaction price per treatment against that period’s second-lowest cost. The secondprice auction prices in red circles are highly correlated with the second-lowest cost, for both the 

 

13 cf. 10. 
13

two-seller and four-seller treatments, which is consistent with the sellers’ unique dominant 

strategy in the second-price auction. Moreover, a 95% prediction interval for a linear regression 

of the second-price auction prices on the second-lowest cost contains the 45° line, which 

corresponds to bidding according to the dominant strategy.14 In marked contrast, the verifiable 

negotiation prices in blue diamonds are not strongly correlated with the second-lowest cost. In 

fact, many of the verifiable negotiation prices are less than the second-lowest cost and lie outside 

the aforementioned 95% prediction interval. Thus, while the behavior in the second-price 

auctions is consistent with the sellers’ playing their dominant strategy, it does not reliably predict 

the prices in the verifiable negotiations, which are lower. 

Having shown the nature of the across-treatment price difference, we can now explain 

why the verifiable multilateral negotiation prices are less than the second-price auction prices. 

Figure 3 plots the winning seller’s initial offer against the second-lowest cost for each period of 

verifiable negotiations in all sessions. The initial offer of the winning seller (nearly always the 

low-cost seller, as illustrated by the efficiency results in Finding 3) is often less than the secondlowest cost. Consequently, in those instances there was no actual negotiation of prices, and the 

price is less than the corresponding price in the second-price auctions. In the Appendix we 

provide some examples from the negotiation transcripts of the sellers’ offering behavior and the 

negotiated prices. These examples illustrate the price movement, or lack thereof, as a function of 

the initial offer’s relationship to the second-lowest cost. 

The hypothesized theoretical equivalence of second-price auctions and verifiable 

multilateral negotiations relies on the crucial assumption that sellers make nonserious initial 

offers at the buyer’s value (6.00), so that offers subsequently decline. Figure 3 illustrates that 

this clearly is not how the sellers behave. Sellers submit initial offers at prices greater than their 

costs, but generally less than 6.00. One possible consequence of this behavior is that when the 

gap between the lowest and second-lowest cost is large, the low-cost seller’s initial offer may be 

less than the second-lowest cost, resulting in second-price auction prices exceeding negotiated 

prices. When the gap between the lowest and second-lowest cost is small, the low-cost seller’s 

initial offer is likely to exceed the second-lowest cost. In that instance, negotiated prices and 

 

14 Obviously, the sellers are not strictly bidding according to their dominant strategy, because the transaction prices 

are somewhat higher than the second-lowest cost. 
14

second-price auction prices are similar, as the winning offer is competed down to the secondlowest cost. 

Table 4 reports the results of a test supporting this “gap” explanation using an OLS 

regression of the difference between the average second-price auction price and the average 

verifiable negotiation price on the lowest cost, second-lowest cost, and regime dummy variable 

interactions. The price difference between the second-price auctions and the multilateral 

negotiations increases as the lowest cost decreases, holding the second-lowest cost constant. 

Similarly, the price difference between the second-price auctions and the multilateral 

negotiations increases as the second-lowest cost increases, holding the lowest cost constant. 

The preceding results illustrate one reason to perform laboratory tests of theoretical 

predictions. If one considered verifiable multilateral negotiations to be like English auctions, 

then their predicted outcomes would be identical to the outcomes of second-price auctions. 

However, we find that the two institutions’ outcomes differ when the sellers are responsible for 

making the initial offer, because the sellers’ initial offers are less than the English auction’s 

starting price, which is the buyer’s value. This negotiating behavior may be explained by the 

sellers’ rates of time preference, as they may be trying to hasten the negotiations by making 

aggressive initial offers.15 

5. Across-Experiment Results 

 We designed this experiment to be comparable to the one reported in Thomas and Wilson 

[2001], which evaluates and compares behavior in first-price auctions and nonverifiable 

multilateral negotiations. That experiment was conducted in the same manner as the present one, 

with the following institutional differences. In the first-price auction, sequences of which are 

denoted by F, the seller offering the lowest price wins the auction and is paid the price it offered. 

In the nonverifiable multilateral negotiation, sequences of which are denoted by N, the sellers are 

not informed via the mechanism of the buyer’s best current offer. Thus, whatever claims about 

competing offers the buyer makes in its communications with the sellers cannot be verified. We 

limit our across-experiment analysis to the first twelve periods (Regime 1), in which subjects 

have no prior experience with any of the four institutions, because the results of the earlier 

 

15 It also does not appear that this effect diminishes as the sellers gain experience. 
15

experiment exhibited permanent institutional influences in later rounds that are not present here. 

We denote the expected price in institution k by Pk (k = F, N, S, V). 

Finding 4: In Regime 1, prices are weakly lowest in first-price auctions, followed in order by 

nonverifiable multilateral negotiations, verifiable multilateral negotiations, and second-price 

auctions. With two sellers, the ranking of transaction prices is PF < PN = PV < PS. With four 

sellers, the ranking of transaction prices is PF = PN < PV < PS. 

Evidence: Table 5 reports the results of a linear mixed-effects analysis that combines the 16 

sessions in Thomas and Wilson [2001] with the 16 reported here, with the transaction price as 

the dependent variable. The two fixed effects that are not self-explanatory are defined as 

follows: Negotiation equals 1 for nonverifiable and verifiable multilateral negotiation sessions 

and equals 0 otherwise, and Verifiable equals 1 for verifiable multilateral negotiation sessions 

and equals 0 otherwise. Thomas and Wilson [2001] find that PF = PN with four sellers, and that 

PF < PN with two sellers.16 In Finding 2 above we find that PV < PS with both two and four 

sellers. That PN < PV with four sellers is captured by the Verifiable fixed effect, which measures 

how much four-seller verifiable multilateral negotiation prices differ from four-seller 

nonverifiable multilateral negotiation prices. We find that four-seller verifiable multilateral 

negotiation prices exceed four-seller nonverifiable multilateral negotiation prices by 3 β

ˆ = 0.613, 

which is significant (p-value = 0.0345). For the two-seller treatment, the sum of the Verifiable

and Two × Verifiable coefficients captures how much two-seller verifiable multilateral 

negotiations differ from two-seller nonverifiable multilateral negotiations. We find that 

3 6 β

ˆ βˆ + = –0.29, which is insignificant at conventional confidence levels (p-value = 0.2555).

The most interesting aspect of Finding 4 is that credible verification of offers has no 

effect on prices in multilateral negotiations with two sellers, but it increases prices with four 

sellers. One way to understand this result is to consider the first-price auction and second-price 

auction as baseline polar cases. Behavior in the first-price auction reflects sellers’ concern and 

lack of information about their rivals’ price-setting behavior. In contrast, behavior in the secondprice auction reflects sellers’ lack of concern about their rivals’ price-setting, which follows from 

the existence of a dominant strategy. In the verifiable multilateral negotiations, sellers are well 
16

informed about their rivals’ price-setting and consequently set higher prices than in the first-price 

auctions. In the nonverifiable multilateral negotiations, the sellers’ lack of concrete information 

about their rivals potentially influences behavior. 

In the four-seller nonverifiable multilateral negotiation, having three rivals taking hidden 

actions is sufficient to induce behavior as aggressive as in the corresponding first-price auction. 

However, in the two-seller setting, having only a single rival acting secretly does not induce such 

aggressive behavior. In Thomas and Wilson [2001], we find that the divergence in outcomes of 

the first-price auction and nonverifiable multilateral negotiation with two sellers is driven by 

occasions in which there is a large gap between the lowest and second-lowest cost. It appears 

that in negotiations with two sellers, a seller with low costs is sufficiently confident about the 

likelihood its rival has high costs that the additional information available in the verifiable 

multilateral negotiations has relatively little value. Hence, the prices are the same in both 

negotiation formats. In contrast, the additional information increases the sellers’ prices and 

profits when there are four sellers. 

6. Conclusion 

In this paper we use the experimental method to examine how the verifiability of offers 

affects both the outcomes of multilateral negotiations, and the relationship between the outcomes 

of multilateral negotiations and of different auction formats. At the within-experiment level, 

with both two and four sellers we find that transaction prices are statistically lower in verifiable 

multilateral negotiations than in second-price auctions, but that the institutions are equally 

efficient. Sellers in the second-price auctions largely follow their unique dominant strategy, so 

the market price is approximately equal to the second-lowest cost. Prices are lower in the 

verifiable multilateral negotiations, because in some instances the low-cost seller’s initial offer is 

below its next-closest rival’s cost, which eliminates the need for further negotiation. This 

unanticipated behavior contradicts in part our hypothesis that the two institutions would have 

identical outcomes. 

At the across-experiment level, with both two and four sellers we find a consistent 

ranking of transaction prices across the four institutions. Prices are always lowest in first-price 

auctions, followed in turn by nonverifiable negotiations, verifiable negotiations, and second-

 16 This is reaffirmed in Table 5 with 2

ˆ

β = –0.00 (p-value = 0.9974) and 5

ˆ

β = 0.79 (p-value = 0.0521), respectively. 
17

price auctions. Second-price auction prices always strictly exceed the other prices. With two 

sellers, nonverifiable and verifiable negotiation prices are statistically indistinguishable, while 

with four sellers, first-price auction and nonverifiable negotiation prices are statistically 

indistinguishable. 

In addition to providing evidence about behavior in multilateral negotiations, our results 

have implications for institutional design. First, we find that providing sellers with more 

information about their rivals’ price-setting behavior surprisingly leads to higher rather than 

lower prices in multilateral negotiations. Moreover, this difference would be even larger if the 

verifiable multilateral negotiations began with nonserious offers at the buyer’s value, as then the 

prices in the verifiable negotiations would be even higher. This price ranking is reminiscent of 

the price ranking of second-price and first-price auctions. One could argue that in both firstprice auctions and nonverifiable multilateral negotiations, similar factors contribute to the 

sellers’ being more aggressive in their price-setting behavior, relative to the dominance-solvable 

second-price auctions and to the more informationally rich verifiable multilateral negotiations. 

Second, we find that buyers in our setting should prefer to employ first-price auctions 

rather than either type of multilateral negotiation, assuming that multilateral negotiations are 

more costly than auctions in terms of the time spent determining the transaction price. As the 

latter assumption appears reasonable, this conclusion raises the question of why first-price 

auctions are not observed more frequently in common transactions. One explanation is that 

reputation effects create a barrier for buyers trying to implement first-price auctions. For 

example, a car buyer is a short-run player in the market for new automobiles, and hence is 

unlikely to be concerned about maintaining a reputation. If the car buyer approaches several 

dealers and tells them that he wants their best offer, as in a first-price auction, then the sellers 

would be foolish to actually submit their first-price offers. If the buyer thought he had received 

first-price offers, then he still would want to haggle with the dealers. Moreover, the dealers 

might be willing to make concessions if asked, because each knows that if he currently has the 

second-lowest offer, then he may yet get a profitable sale by reducing his price. Thus, the 

buyer’s inability to commit to the procurement format likely inhibits his use of what appears to 

be the preferred institution. In our experiment, the buyer was exogenously committed to this 

format, which provided a constraint on his behavior that likely does not generally exist in actual 

transactions. 
18

The implications of our results and inferences about their generality are limited by the 

scope of our experiment and would benefit from further research. First, it would be useful to 

extend our analysis to settings with different numbers of sellers or with asymmetries across 

sellers. Second, it would be interesting to let the buyer select his preferred institution, or be 

unable to commit not to haggle upon receiving the sellers’ initial offers. Third, if participation is 

costly, then any comparison of institutions must consider the sellers’ incentives to participate. 
19

References 

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the Dutch-First Auction Non-Isomorphism,” Journal of Economic Behavior and 

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Cox, J., Smith, V., and Walker, J. (1988). “Theory and Individual Behavior of First-Price 

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Kagel, J., Harstad, R., and Levin, D. (1987). “Information Impact and Allocation Rules in 

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McAfee, R.P., and McMillan, J. (1987). “Auctions and Bidding,” Journal of Economic 

Literature 25, 699-738. 

McAfee, R.P., and McMillan, J. (1996). “Analyzing the Airwaves Auction,” Journal of 

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Econometrica 50, 1089-1122. 

Roth, A., and Ockenfels, A. (2001). “Last-Minute Bidding and the Rules for Ending SecondPrice Auctions: Evidence from eBay and Amazon Auctions on the Internet,” American 

Economic Review, forthcoming. 
20

Smith, V. (1962). “An Experimental Study of Competitive Market Behavior,” Journal of 

Political Economy 70 (2), 111-137. 

Thomas, C.J., and Wilson, B.J. (2001). “A Comparison of Auctions and Multilateral 

Negotiations,” RAND Journal of Economics, forthcoming. 

Waehrer, K., and Perry, M. (1999). “The Effect of Mergers in Open Auction Markets.” 

unpublished manuscript. 

Wolfram, C. (1998). “Strategic Bidding in a Multiunit Auction: An Empirical Analysis of Bids 

to Supply Electricity in England and Wales,” RAND Journal of Economics 29, 703-725. 

Table 1. Average Transaction Price, Nash Predicted 

Second-Price Auction Price*, and Efficiency** 

Sequence Two Sellers Four Sellers 

SSVS 

Observed 

Price 

Nash 

Prediction 

Observed 

Efficiency 

Observed 

Price 

Nash 

Prediction 

Observed 

Efficiency 

Periods 1-12: S 4.17 3.62 98.1% 3.03 2.61 97.5% 

Periods 13-28: S 4.49 4.26 98.7% 2.87 2.67 96.8% 

Periods 29-40: V 2.53 3.90 93.8% 1.62 2.71 95.0% 

Periods 41-46: S 4.89 4.63 99.3% 2.63 2.44 99.3% 

 

VSSV 

Periods 1-12: V 3.46 3.62 96.9% 2.50 2.61 93.6% 

Periods 13-28: S 4.69 4.26 97.9% 3.19 2.67 98.1% 

Periods 29-40: S 4.03 3.90 97.6% 3.04 2.71 97.0% 

Periods 41-46: V 3.35 4.63 95.6% 1.85 2.44 95.6% 

 *The Nash predicted second-price auction prices are conditional on the cost draws. 

 ** Efficiency is defined to be 100% × (6 – winner’s cost)/(6 – lowest cost draw). 
21

Table 2. Estimates of the Linear Mixed-Effects Model for Price 

 where ~ (0, ), ~ (0, ).

,

2

2,

2

1

1 2 3

i ij i

ij i i i i i ij

e N N

Price e Two Verifiable Two Verifiable

σ ε σ

= μ + + β + β + β × + ε

 

Estimate

Std. 

Error 

Degrees of 

Freedom* t-statistic p-value

Regime 1: Periods 1 – 12 

 

μ 3.080 0.179 176 17.251 0.0000 

Two 1.133 0.299 12 3.787 0.0013†

Verifiable -0.590 0.257 12 -2.300 0.0402 

Two × Verifiable -0.119 0.389 12 -0.305 0.7652 

 192 Obs. 

 Ha: β2 + β3 ≠ 0 0.0319 

Regime 2: Periods 13 – 28 

 

μ 2.886 0.168 240 17.159 0.0000 

Two 1.608 0.238 12 6.747 0.0000†

Verifiable History 0.409 0.221 12 1.845 0.0898 

Two × Verifiable History -0.119 0.310 12 -0.386 0.7066 

 256 Obs. 

 Ha: β2 + β3 ≠ 0 0.2069 

Regime 3: Periods 29 – 40 

 

μ 3.210 0.245 174 13.085 0.0000 

Two 0.824 0.354 12 2.330 0.0191†

Verifiable -1.621 0.342 12 -4.734 0.0005 

Two × Verifiable 0.060 0.515 12 0.116 0.9095 

 190‡

 Obs. 

 Ha: β2 + β3 ≠ 0 0.0016 

Regime 4: Periods 41 – 46 

 

μ 2.669 0.240 80 11.144 0.0000 

Two 2.258 0.364 12 6.200 0.0000†

Verifiable -0.726 0.342 12 -2.125 0.0276†

Two × Verifiable -0.671 0.498 12 -1.348 0.2025 

 96 Obs. 

 Ha: β2 + β3 < 0 0.0012†

*N.B. The linear mixed effects model for repeated measures treats each session as one degree of 

freedom with respect to the treatments. Hence, with four parameters, there are 12 degrees of freedom 

for the estimates of the treatment fixed effects (16 sessions – 4 parameters). 

†

One-sided test. 

‡

There were two cases in which the buyer did not accept any offer, both in the two-seller treatment 

when both sellers’ costs were relatively high. 

Note: The linear mixed-effects model is fit by maximum likelihood. For brevity, the session random 

effects are not included in this table or any others. 
22

Table 3. Estimates of the Linear Mixed-Effects Model for Efficiency 

 where ~ (0, ), ~ (0, ).

,

2

2

2

1

1 2 3

σ ε σ

μ γ γ γ ε

e N N

Efficiency e Two Verifiable Two Verifiable

i ij

ij i i i i i ij = + + + + × +

 

Estimate

Std. 

Error 

Degrees of 

Freedom* t-statistic p-value

Regime 1: Periods 1 – 12 

 

μ 97.51 1.43 176 68.05 0.0000 

Two 0.61 2.03 12 0.30 0.7697 

Verifiable -3.93 2.03 12 -1.94 0.0764 

Two × Verifiable 2.67 2.87 12 0.93 0.3702 

 192 Obs. 

 Ha: γ2 + γ3 ≠ 0 0.5456 

Regime 2: Periods 13 – 28 

 

μ 96.75 1.40 240 68.88 0.0000 

Two 1.94 1.99 12 0.98 0.3479 

Verifiable History 1.34 1.99 12 0.67 0.5133 

Two × Verifiable History -2.17 2.81 12 -0.77 0.4539 

 256 Obs. 

 Ha: γ2 + γ3 ≠ 0 0.6812 

Regime 3: Periods 29 – 40 

 

μ 97.02 2.11 176 45.90 0.0000 

Two 0.60 2.99 12 0.20 0.8432 

Verifiable -2.00 2.99 12 -0.67 0.5170 

Two × Verifiable -1.81 4.23 12 -0.43 0.6764 

 192 Obs. 

 Ha: γ2 + γ3 ≠ 0 0.2273 

Regime 4: Periods 41 – 46 

 

μ 99.25 2.34 80 42.47 0.0000 

Two 0.02 3.31 12 0.01 0.9950 

Verifiable -3.64 3.31 12 -1.10 0.2923 

Two × Verifiable -1.69 4.67 12 -0.36 0.7236 

 96 Obs. 

 Ha: γ2 + γ3 ≠ 0 0.1326 
23

Table 5. Across-Experiment Estimates of the Linear Mixed-Effects Model for Price

 where ~ (0, ), ~ (0, ).

 ,

 

2

2,

2

1

6 7

4 5

1 2 3

i ij i

i i i i ij

i i i

ij i i i i

e N N

Two Verifiable Two 2ndPriceAuction

2ndPriceAuction Two Negotiation

Price e Two Negotiation Verifiable

σ ε σ

β β ε

β β

μ β β β

+ × + × +

+ + ×

= + + + +

 

Estimate

Std. 

Error 

Degrees of 

Freedom t-statistic p-value

Regime 1: Periods 1 – 12 

 

μ 1.875 0.190 350 9.885 0.0000 

Two 1.129 0.295 24 3.821 0.0004†

Negotiation -0.001 0.266 24 -0.003 0.9974 

Verifiable 0.613 0.274 24 2.242 0.0345 

2ndPriceAuction 1.199 0.272 24 4.407 0.0002 

Two × Negotiation 0.786 0.385 24 2.044 0.0521 

Two × Verifiable -0.898 0.367 24 -2.448 0.0220 

Two × 2ndPriceAuction 0.007 0.435 24 0.016 0.9871 

 Ha: β3 + β6 ≠ 0 0.2555 

 382 Obs. 

†

One-sided test. 

Table 4. OLS Regression of the Difference of 

Average Second-Price Auction and Average Verifiable Negotiation Prices 

Variable* Estimate Std. Error t-statistic p-value 

Intercept -0.21 0.17 -1.22 0.2279 

Lowest Cost -0.34 0.13 -2.69 0.0096 

Second-Lowest Cost 0.48 0.09 5.20 0.0000 

Lowest Cost × Regime 3 -0.38 0.15 -2.47 0.0166 

Second-Lowest Cost × Regime 3 0.37 0.10 3.69 0.0005 

Lowest Cost × Regime 4 -0.13 0.21 -0.64 0.5217 

Second-Lowest Cost × Regime 4 0.09 0.12 0.77 0.4470 

Adj. R2 = 68.7% 

Obs.= 60 = 30 periods × 2 (Two vs. Four)

*An F7,46-test for 7 other variables including the dummy variables Two and Regimes 3 and 4, and 

their interactions with Lowest Cost and Second-Lowest Cost, indicates that they are jointly 

insignificant (p-value= 0.5036). 
24

Regime 1

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

1 2 3 4 5 6 7 8 9 10 11 12

Period

Transaction Price

Two Sellers, VSSV

Two Sellers, SSVS

Four Sellers, VSSV

Four Sellers, SSVS

Regime 2

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

13 15 17 19 21 23 25 27

Period

Transaction Price

Two Sellers, VSSV

Two Sellers, SSVS

Four Sellers, VSSV

Four Sellers, SSVS

Regime 3

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

29 30 31 32 33 34 35 36 37 38 39 40

Period

Transaction Price

Two Sellers, VSSV

Two Sellers, SSVS

Four Sellers, VSSV

Four Sellers, SSVS

Regime 4

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

41 42 43 44 45 46

Period

Transaction Price

Two Sellers, VSSV

Two Sellers, SSVS

Four Sellers, VSSV

Four Sellers, SSVS

Figure 1. Average Transaction Prices By Regime 
25

Linear Fit

Second-Price Auction Prices = 0.81+0.88*Second-Lowest Cost

R2

 = 91.9%

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Second Lowest Cost

Average Price

Second-Price Auction Prices

Verifiable Negotiation Prices

Dominant Strategy Prediction

95% Prediction Interval

Panel (a) Two-Seller Treatment 

Linear Fit

Second-Price Auction Prices = 0.82 +0.82*Second-Lowest Cost

R2

 = 93.6%

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Second Lowest Cost

Average Price

Second-Price Auction Prices

Verifiable Negotiation Prices

Dominant Strategy Prediction

95% Prediction Interval

Panel (b) Four-Seller Treatment 

Figure 2. Average Transaction Price versus Second-Lowest Cost 
26

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Second Lowest Cost

Initial Offer of Winning Seller

VSSV2s1

VSSV2s2

VSSV2s3

VSSV2s4

SSVS2s1

SSVS2s2

SSVS2s3

SSVS2s4

45o

Panel (a) Two-Seller Treatment 

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Second Lowest Cost

Initial Offer of Winning Seller

VSSV4s1

VSSV4s2

VSSV4s3

VSSV4s4

SSVS4s1

SSVS4s2

SSVS4s3

SSVS4s4

45o

Panel (b) Four-Seller Treatment 

Figure 3. Winning Seller’s Initial Offer versus Second-Lowest Cost 
27

Panel (a) Two-Seller Treatment 

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Minimum Cost

Average Price

Four Sellers, NFFN

Four Sellers, VSSV

Linear Trends

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Minimum Cost

Average Price

Two Sellers, NFFN

Two Sellers, VSSV

Linear Trends

Panel (a) Two-Seller Treatment 

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Minimum Cost

Average Price

Four Sellers, NFFN

Four Sellers, VSSV

Linear Trends

Panel (b) Four-Seller Treatment 

Figure 4. Average Price versus Minimum Cost in Verifiable and Nonverifiable 

Multilateral Negotiations (Regime 1) 
28

Appendix 

The following selections are the written negotiations from the real-time ordered transcript and 

the descriptions of the offering activity. They illustrate that when the initial offer of the low-cost 

seller (o1) is greater than the second-lowest cost (c(2)) the final price is equal to the second-lowest 

cost. However, when the initial offer for the low-cost seller is less than the second-lowest cost, 

the final price is the initial offer of the low-cost seller. 

Examples when o1 > c(2)

Four Seller VSSV, Session 2

Seller 3’s initial offer was 2.50 with a cost of 0.80. 

Seller 4’s initial offer was 10.00 with a cost of 0.10. 

Seller 1’s cost was 1.00. 

Seller 2’s cost was 5.54. 

Final price is 0.80, paid to Seller 4. 

PERIOD 3 

[Seller 1]: I split the profit 50/50. 

[Buyer to Seller 1]: 3 in l\the lead 

[Buyer to Seller 2]: 3 still has it 

[Seller 1]: How about this? 

[Buyer to Seller 4]: come on man, you gotta be kidding me 

[Seller 2]: 2.50 -- why? 

[Seller 2]: why so low? 

[Buyer to Seller 1]: Good, your almost there 

[Buyer to Seller 2]: Don’t know, I’m just the buyer 

[Seller 2]: loosing profit... 

[Buyer to Seller 3]: you want it? 

[Seller 3]: yeh 

[Buyer to Seller 2]: Going for broke? 

[Buyer to Seller 4]: Wow 

[Seller 1]: Man! I can’t go for least than it 

[Seller 1]: 

[Seller 2]: common...this is a joke.... 

[Buyer to Seller 2]: I know, I have to watch out for my interests though 

[Seller 2]: .60??? 

[Buyer to Seller 4]: Alright, its yours 

Two Seller VSSV, Session 2

Seller 1’s initial offer was 4.80 with a cost of 1.53. 

Seller 2’s initial offer was 5.50 with a cost of 4.70. 

Seller 2 drops price to 4.79. 

Seller 1 responds with 4.70. 

Seller 2 matches 4.70 (at cost). 

Final price is 4.70 (buyer buys from Seller 1 who first offered 4.70). 

PERIOD 5 

[Buyer to Seller 2]: no way 

[Buyer to Seller 2]: keep going or no business 

[Seller 2]: gotta cover my costs here 
29

Examples when o1 < c(2)

Four Seller SSVS, Session 3

Seller 1’s initial offer was 0.90 with a cost of 0.37. 

Seller 3 had the second-lowest cost at 4.07. 

Seller 2’s cost was 5.73. 

Seller 4’s cost was 4.11. 

Final price is 0.90. 

PERIOD 38 

[Seller 2]: how do you like the product 

[Seller 3]: i lose 

[Buyer to Seller 1]: i think this time u really need money 

[Buyer to Seller 2]: i hate it man..too much 

[Seller 2]: well what’s the price that u want it at 

[Buyer to Seller 3]: y u will see 4.20 the highest 

[Buyer to Seller 2]: seller 1 is selling at .85 

[Seller 1]: i think you’re the one who wants the money :) 

[Seller 2]: aites..go for it then! 

[Buyer to Seller 1]: thaz y ur charging high 

[Seller 3]: just buy it at the .90 offer you have 

[Buyer to Seller 3]: its .80 

[Seller 3]: no it isnt i can see the lowes submitted ask 

[Buyer to Seller 1]: man u will surely lose..i will buy froom u if ur price comes 15 cents ..down 

[Seller 1]: how about five cents 

[Buyer to Seller 1]: 10 cents..do it no time..or bye 

[Seller 1]: seven cents 

[Buyer to Seller 1]: okay 

[Seller 3]: its stilll .90 

Two Seller VSSV, Session 1

Seller 1’s initial offer was 3.00 with a cost of 1.53. 

Seller 2’s initial offer was 5.00 with a cost of 4.70. 

Final price is 3.00. 

PERIOD 5 

No written negotiation. Seller 2 cannot compete with an offer of 3.00 and so the buyer accepts Seller 1’s 

initial offer. 

Four Seller VSSV, Session 2

Seller 1’s initial offer was 4.00 for a cost of 3.95. 

Seller 2’s initial offer was 4.82 for a cost of 4.77. 

Seller 3’s initial offer was 6.00 for a cost of 5.98. 

Seller 4’s initial offer was 2.00 for a cost of 1.21. 

Final price is 2.00. 

PERIOD 12 

No written negotiation. Sellers 1,2, and 3 cannot compete with an offer of 2.00 and so the buyer accepts 

Seller 4’s initial offer.