Discussion Paper No. 819

BEHAVIORAL EFFICIENCY II:
A SIMPLE LABORATORY DEMONSTRATION

Ronald M. Harstad

October 2011

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, JapanBehavioral Efficiency II:
A Simple Laboratory Demonstration 1
Ronald M. Harstad

University of Missouri
harstad@missouri.edu
ISER, Osaka University
October 9, 2011
Please consult before citing or circulating
Abstract
Laboratory experiments reporting on shortfalls from allocative efficiency of allocation
mechanisms depend on the induced-values methodology, which cannot be extended to thefield. Harstad [2011] proposes to observe efficiency of allocation mechanisms without
knowing motivations via behavior in appropriately designed aftermarkets. This paper
demonstrates the approach in a highly simplified economy: allocation of a single unit of an
abstract commodity. In the context studied, second-price auctions are observed to yieldsignificantly greater behavioral inefficiencies than first-price auctions, both in terms offrequency of behaviorally inefficient outcomes, and in terms of the expected size of gains
from aftermarket trade missed by the auction itself. The design is shown to be field-ready.

	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
1 The Economic Science Laboratory at the University of Arizona provided facilities, recruiting and assistancefor the conduct of the experiments; thanks to Cathleen Johnson and Lana Sooter for managing this. The J
Rhoads Foster Professorship Endowment of the University of Missouri and the Freshwater Group Research
Fund of the University of Arizona provided appreciated financial support, and the Institute for Social andEconomic Research at Osaka University provided hospitality during the writing. I thank Eric Cardella,
Raymond Chiu, Anthony Dubis and Richard Kiser for assistance in programming and conducting theexperiments, and Katsunori Yamada for suggestions and assistance in data analysis.

1. Introductory Notes
Recommendations for policy adoption or alteration are more valuable if evidence of thesize of shortfalls from allocative efficiency can be provided for the allocation mechanisms or
policy instruments under consideration. Such evidence has so far come from laboratory
experiments using an induced-values methodology for, e.g., an abstract commodity.2 Thatmethodology requires that experimental subjects’ motivations are known to theexperimenter, and as such is unavailable for field experiments.
In the preceding methodology paper, Harstad [2011], I define behavioral efficiency: an
outcome of an allocation mechanism is said to be behaviorally efficient if an appropriate
aftermarket is actually appended to the allocation mechanism and at most a negligible
aggregate size of mutually beneficial gains is observed on the aftermarket. That is, a field
experiment can first observe behavior under an allocation mechanism (even an informal orculturally-based method of reaching an allocation), and then append a properly constructed
aftermarket, and draw inferences from aftermarket behavior as to whether the field
experiment’s subjects perceived any remaining mutually beneficial transactions. That paper
also characterizes construction of an incentive compatible, transparent aftermarket.
This paper is a first demonstration of the concept, providing a concrete example of theappropriate usage of a properly constructed aftermarket to observe allocative efficiencies (orshortfalls therefrom) without relying on knowing subjects’ motivations. It finds first-priceauctions less behaviorally inefficient than second-price auctions, measures efficiency
shortfalls; in this context, subjects’ bidding was unaffected by knowing there would be anaftermarket.
2. Laboratory Setting
Five-bidder sealed-bid auctions of a single abstract asset were conducted, in sevensessions (110 subjects) via first-price rules, and in six sessions (85 subjects) via second-pricerules.3 There were generally 10, 15, 20, 25 or 30 subjects in the laboratory during a session,
with random reassignments into groups of five each period.4
Affiliated asset valuations (Milgrom and Weber [1982]) for subjects were determined asfollows. In each period, first a random number C, called a central tendency, was drawn
uniformly from [$50, $1000] (all random variables are multiples of $0.01). Then, given a
realization c of C, for each subject j an estimate Xj was drawn uniformly from [$(c – 10),$(c + 10)], conditionally independent. Finally, asset value to subject j was Vj = (3/4)Xj +(1/4)C; this system incorporates private values (the first term, Xj) to introduce efficiency
issues, as well as a natural, small common-value component (C).5 These rules were carefully
	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
2 A subject j might, for example, be told that she is one of N buyers or M sellers of an abstract good called X

that will be traded, with her payoff being the difference between trading prices and induced values, as in “thefirst unit of X you buy can be resold to the experimenter for $8.75, the second for $6.80, the third for $5.10” toa potential buyer, or “the first unit of X you sell can be obtained from the experimenter for $3.10, etc.”
3 Thus, comparisons across pricing rules are between-subject comparisons.
4 Subjects were University of Arizona undergraduates, recruited campuswide via website, and sat at visually
isolated computers. A second-price auction session for which less than ten subjects showed was eliminatedfrom data analysis. The experiments were conducted in October and November 2009, using the Z-Treeprogramming environment (Fischbacher [2007]).
5 A principal reason for including a common-value component was to avoid a throw-away bid problem: withindependent private values, most values will yield so low a chance of winning as to make serious consideration

	
  

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explained and examples given. C was not revealed to subjects until end-of-period feedback,which gave a complete, anonymous report of C, Xj’s, Vj’s, all behavior, and profit
calculations. The instructions stated that a reserve price, below which the asset would not besold, was drawn anew before each auction, uniformly from [$(c – 10), $(c – 6)], and would
not be revealed until end-of-period feedback.6
Subjects began the experiment with a bank balance of $12, with profits added and losses
subtracted during the session, and the final balance paid in cash. These valuation procedures
call for a small winner’s curse correction; the 90% confidence interval for the loss in theevent a winning bid exceeded the symmetric, risk-neutral equilibrium bid by exactly thewinner’s curse correction (were all rival bids in equilibrium) is about [$1.50, $4.25]. Thus,
three to four such losses could likely be handled without the balance going negative.7
3. Methodology Implementation
To discern from subjects’ behavior whether an auction attained an efficient outcome, theexperiment appended an aftermarket designed as follows. Once all subjects had typed andsubmitted their bids, the winning bidder was determined (throughout by fair random tie
breaking if necessary). Then each bidder was informed of the price determined in theauction and whether his bid acquired or did not acquire the asset. Some seconds later, theaftermarket that, before bidding, the subjects had been told would follow the auction was
begun.
A price clock ticked up on all subjects’ screens, rising by $0.25 every two seconds (thoughmore slowly in the first period with an aftermarket), beginning at a random price calculated
to be acceptable to all subjects but noisy enough to avoid revealing information about thestill-unknown C. The bidder who acquired the asset was labeled the offerer, and asked to click
the “Accept” button on the screen when the price reached the lowest price at which he waswilling to sell the asset just acquired in the auction to one of the losing bidders. Each of thefour bidders that did not submit the highest bid was asked to do nothing so long as theprices being shown were prices at which he would be willing to buy the asset from thewinning bidder, and then to click “Accept” at the highest such price. No subject observed
any information about other subjects’ behavior in the aftermarket until all five had clicked ona price.
Instructions had carefully described the rules relating these Accept Bids (of the fourbidders who did not acquire the asset) and Accept Ask (of the acquirer) to possible
aftermarket transactions. [1] If the offerer’s Accept Ask exceeds all four Accept Bids, there
is no aftermarket transaction. [2] If at least two Accept Bids are no lower than the Accept
Ask, the asset is transferred from the offerer to the bidder selecting the highest Accept Bid,
at a price set by the second-highest Accept Bid. [3] If the highest Accept Bid exceeds the
Accept Ask and it exceeds all other Accept Bids, a random number R, drawn before the
	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
of what to bid not worthwhile. Unfortunately, how high a value a subject has to draw before he or she chooses
to pay attention is unobservable. In the current design, all estimates between $60 and $990 have the same
expected profitability, removing throwaway bid concerns. (Data analysis only includes the cases, almost 99%,
where subjects’ estimates were in the [$60, $990] range.)
6 As expected, the reserve price was never binding.
7 If a subject’s balance became negative, he was given a $20 loan to be repaid out of his final bank balance. Twoof 195 subjects could not quite repay the loan; it was of course forgiven and they were paid only the usual $5
show-up fee.

	
  

3

auction from multiples of $0.01 in [$c, $(c + 15)] equiprobably, determines the aftermarket
outcome. If R falls between the highest Accept Bid and the Accept Ask, the asset istransferred from the offerer to the bidder selecting the highest Accept Bid, at a price set
equal to R; otherwise, there is no aftermarket transaction.
This aftermarket design justifies the inferences about behavioral efficiency to be drawn
from observations of aftermarket behavior: any mutually beneficial trade revealed istransacted with positive probability, and in no aftermarket transaction is the pricedetermined by the behavior of either transacting party. Among possible aftermarket designs,
prior experimental evidence (Harstad [2000]) suggests the use of the price clock makes
aftermarket incentives as transparent as possible. Whenever at least one bidder who did notacquire the asset in the auction selects an Accept Bid above the offerer’s Accept Ask, amutually beneficial trade that the auction did not achieve has been identified (whether or not
the aftermarket actually transacts that trade).
4. Session Protocol
Each experimental session ran 150 minutes and followed a multi-phase protocol, to build
the desired treatment step-by-step from simpler games. After instructions regarding thewhole session and the first phase, that first phase exposed subjects to the software of theaftermarket, without introducing the word “aftermarket.” In phase 1 (4-5 periods), eachsubject was informed of a list of all five private values of the abstract asset (told which was
his value), which were drawn i.i.d. uniform on [$5, $10]. Per instructions, one subject waschosen at random to be the offerer, the others bidders.8 As just described, the offerer was
asked to click on an Accept Ask, the four bidders to click on Accept Bids. Then theaftermarket rules above were used to determine payoffs for the period, which were simply
asset value minus transaction price for the buyer, and transaction price minus asset value forthe seller, if there was a transaction, and zero for all non-transacting subjects.
Further instructions were distributed and read before each following phase. Phase 2 (6-7
periods) introduced private information, with subjects’ private values first revealed to allgroup members (anonymously) during end-of-period feedback. Phase 3 (6-7 periods)
introduced two changes: [i] all five subjects were now bidders asked to select Accept Bids
(that is, in a closed-clock variant of an English auction), and [ii] the private values were now
affiliated (as in section 2, except that Vj = Xj). Phase 4 (6-7 periods) set aside the priceclock, introducing bidding in a sealed-bid auction (first- or second-price, depending on thesession). Phase 5 (8-11 periods) introduced affiliated values, the Vj = (3/4)Xj + (1/4)C
valuations detailed in section 2.
All this led to the phase of principal interest, phase 6, which re-introduced the softwarefrom the first two phases, but with the offerer being the bidder who acquired the asset in thesealed-bid auction, and the following price-clock activity called an aftermarket. Phase 6 was
generally limited by the time constraint, 6-11 periods. The session ran faster when there
were fewer groups (with the software always waiting for the last subject in the session to bid,
to peruse feedback, etc.); in four of the first-price sessions, we were able to run a final phase
7. Phase 7 had aftermarkets only in even-numbered periods, with the sealed-bid auction the
	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
8 To generate possible gains from trade frequently, the program chose the subject with the highest, second-highest, …, lowest private values with probabilities {1/8, 1/8, ¼, ¼, ¼}.

	
  

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final determination of period profits in odd-numbered periods. In the other nine sessions,
phase 6 was the final phase.
5. Contrasting Predictions
Auction theory predicts aftermarket activity with positive probability following first-priceauctions, but with zero probability following second-price auctions. It is straightforward toshow that the unique, risk-neutral, symmetric Bayesian equilibrium of auction-cumaftermarket (either first- or second-price) is to submit one’s equilibrium bid in the auction
and to select an Accept Bid or Ask in the aftermarket most nearly equal to one’s rational
Bayesian-updated willingness-to-pay or -accept. In this equilibrium, publicly announcing theprice attained in a first-price auction informs each losing bidder (but not the winner) of theamount by which his bid lost. Whenever a bidder lost by a sufficiently small margin, rational
updating leads to his willingness-to-pay exceeding the winning bidder’s willingness-to-accept(as he knows of a second estimate nearly as high as the winning bidder’s estimate, which canbe inferred from the price set by the winner’s monotonic equilibrium bid function).
No similar occurrence is possible following announcement of the price in second-priceauctions. Here the price reveals the private information of the second-highest bidder, who
Bayesian updates on the basis of learning that one rival estimate was higher and three lower,
and this leads to a willingness-to-pay that exceeds his equilibrium bid, while the winningbidder’s updating leads to a willingness-to-accept that is less than his equilibrium bid.
However, the second-price auction equilibrium is envy-free: these two adjustments ofwillingness-to-pay and to accept sum to less than the difference between the two highest
bids, and thus do not change their ordinal rank.9
To my knowledge, prior auction experiments have either induced private values(independent, as in phases 1 and 2, or affiliated, as in phases 3 and 4) or common values(modifying section 2 so that Vj = C, hence there is no inefficiency generated by the bidderwith the highest estimate being outbid). Nonetheless, in both settings, bidders have bid
significantly above the risk-neutral symmetric Bayesian equilibrium (Kagel [1995]), and(more pertinent here) have exhibited more heterogeneity in this overbidding in second-pricethan in first-price auctions.10 Thus, prior laboratory experiment results predict more
aftermarket activity following second-price auctions.
6. Aftermarket ObservationsFirst-price [second-price] auctions were observed to be behaviorally efficient in 72%[57%] of the observations (cf. Table 1). In 28% of 203 first-price auctions, and 43% of 142
second-price auctions, at least one bidder who was outbid was observed to be willing to buy
the asset from the high bidder for mutual gain. (These percentages naturally sum
occurrences where the aftermarket transacted with those where the random price fell below
	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
9 Though stated slightly differently, the results in this and the previous paragraph are not new, and can bepieced together from Milgrom [1981], Milgrom and Weber [1982], and Harstad and Bordley [1996].
Kagel and Levin [1986] report on 199 first-price, common-value auctions, and Kagel, Levin and Harstad[1995] on 154 second-price, common-value auctions. To adjust for varying number of bidders, I calculated astatistic for each session that takes the frequency with which the high signal holder was the high bidder andsubtracts 1/n. The weighted (by number of auctions) average of these statistics was 50.93 for first-priceauctions and 38.73 for second-price auctions.

10

	
  

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the high bidder’s Accept Ask or above the one Accept Bid exceeding that Accept Ask.) Thisdifference is significant at the 1% level in a Pearson test.
Table 1
ObservationsFirst-Price Auctions Second-Price Auctions
1 Aftermarkets Observed

203

142

2 Behaviorally Efficient

72%

57%

3 Mean of Shortfalls

$4.45

$4.16

4 Shortfall Capacity$10.26

5 Aftermarket Fraction

41%

6 Expected Shortfall

$1.24

$1.79

Where aftermarket behavior exhibited such gains, the difference between the most an
outbid bidder will pay and the least the high bidder will accept is a behavioral measure of theshortfall from efficiency, averaged in row 3. While shortfalls when observed were larger infirst-price auctions, when zero shortfalls are averaged in for the behaviorally efficient
outcomes, the expected shortfall in row 6 is smaller for first-price auctions.
It bears emphasis that, while these auctions sold induced-value assets, the behavioral
efficiency and shortfall measures make no use of any information contained in the induced
values. These reports stem solely from subjects’ behaviors: their sealed bids, Accept Bids
and Accept Asks, and in no way depend on any information about subjects’ motivations.
Reports of allocations reached in induced-values experiments can provide efficiency
measures in percentages, because the dollar value of total gains from trade in Pareto-efficient
allocations can be calculated from the induced values. This methodology cannot be used in
the field.
In some situations, behavior in the original allocation mechanism can offer a benchmark
for the economic significance of the size of shortfalls from efficiency. This experimentdemonstrates both the possibility and its limitations.
Second-price auctions are incentive compatible, in that the bid selected determines only
whether the bidder wins or not; the price is solely determined by the highest rival bid. In
particular, the risk-neutral symmetric equilibrium bid is the expected asset value conditioned
on an assumption that the bid is pivotal.11 For the distributions of section 2, this implies thatbids should differ from bidders’ expected values by a constant.12 Hence, differences
between two bids submitted in second-price auctions should be equal to the differences
between the two bidders’ willingnesses-to-pay and therefore measure the gain from trade if
	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
11 For private values, this is the dominant strategy discovered by Vickrey [1961].

This feature of second-price,common-value auctions was first found by Matthews [1977]; the intuition is presented in Harstad and Bordley[1996].
12 This neglects estimates in the ranges [$50, $60] and [$990, $1000], for which the difference is not constant.

	
  

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the asset were hypothetically to be transferred from the lower bidder to the higher bidder.
These observations include 586 differences between a losing second-price bid and the highbid in the same auction. The average of those 586 bid differences is the $10.26 reported inrow 4 above. This is the capacity for shortfalls from efficiency in the sense that, had theoriginal auctions allocated the asset equiprobably among inefficient acquirers, aftermarkets
that reallocated to the efficient acquirer could average $10.26 in gains from trade unattainedby such a complete misallocation to a random inefficient acquirer.
The best measure I can envision to attach an economic significance to the $4.16 mean ofshortfalls revealed by aftermarkets following second-price auctions is that it is 41% of theshortfall capacity.
The absence in Table 1 of a comparable benchmark for first-price auctions is not an
oversight. Differences between a losing first-price bid and the high bid in the same auction
could be averaged. However, without the incentive compatibility of second-price auctions,these first-price bid differences have no similarly strong argument to measure gains fromhypothetical transfers between the bidders: optimizing the {profitability given
winning/probability of winning} tradeoff in the risk-neutral symmetric equilibrium of thefirst-price auction yields a nonlinear term in the bid function (corresponding to the term thatis a constant in second-price auctions). In that equilibrium, if bidder A outbids bidder B by
$8, A’s willingness-to-pay exceeds B’s, but the $8 bid difference is not a measure of thewillingness-to-pay difference.
7. Submitted-Bid Impact
The unique risk-neutral symmetric Bayesian equilibrium of the game consisting of thesealed-bid auction (either pricing rule) followed by the aftermarket is for each bidder tomake the same equilibrium bid as if there were no aftermarket, and then truthfully reveal in
the aftermarket. Despite the theory, it is an empirical question whether subjects bid thesame way when they know an aftermarket will follow; there might be reasons subjects wouldfind for bidding less, or for bidding more, in an auction when knowing there will be anaftermarket.13 The protocol in section 4 is designed to shed light on this question.
The following linear bid function was estimated separately from the first-price andsecond-price data:
Mst = const + βx Experst + βa Aftert + errorst,
where the markup Mst was the observed bid minus the asset value estimate Xst for subject s
in period t; Experst was a control for possible learning effects, the number of periods ofexperience in the affiliated-values auctions; Aftert was a dummy variable taking the value 1 if
the subject knew the auction in period t would be followed with an aftermarket, 0 if thesubject knew the auction would not be followed with an aftermarket.
Estimates obtained from OLS linear regressions with clustering by subject are presented
in Table 2. For both types of auction rules, a null hypothesis that subjects bid no differently
	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
13 Among the possibilities are that a subject might perceive an opportunity to win the auction profitably andthen profit further by selling in the aftermarket, which could be perceived as suggesting more aggressive
bidding than if there were to be no aftermarket; or that a subject might perceive the aftermarket as a second
chance to obtain the asset, which could be perceived as suggesting less aggressive bidding than if there were to
be no aftermarket.

	
  

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when knowing there would be an aftermarket as when there would not cannot be rejected atanything vaguely approaching conventional levels of significance.14
Table 2Estimates
First-Price Data Second-Price Data
const

-2.346-1.435

Std. error(0.567)(1.629)Significance

0.001

0.38

0.045

0.393

Std. error(0.075)(0.370)Significance

0.55

0.29

-1.242-5.063

Std. error(1.431)(4.738)Significance

0.39

0.29

# Observations

2215

1075

F test:

1.24

0.58

0.293

0.562

βx

βa

Significance

8. Distinct Measure?
What can be said about how well behavioral efficiency tracks Pareto efficiency? As theseexperiments used induced values, they can yield insights into the differences between thesemeasures. That is, assume (critically) subjects are all risk-neutral (or identically risk averse),
and assume completeness of the induced motivations (in particular, assume away
interdependent preferences, nonpecuniary preferences, and satiation in cash). Then in a
Pareto-efficient allocation, the asset is acquired by the subject with the highest estimate.
In most observations, when either a first-price or a second-price auction reached aPareto-efficient allocation, behavioral efficiency was observed in the aftermarket, and theinverse: Pareto-inefficient auctions led to behaviorally inefficient outcomes, mutual gains
observed in the aftermarkets.
The two distinctions from tracking were both observed in significant minorities of theobservations. [i] In 15% of first-price auctions and 24% of second-price auctions, the
	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
14 Failure to reject this null was found in alternatives that did not cluster or added subject fixed effects;

alternative where the bid was the dependent variable and asset value estimate an independent variable were
nearly identical.

	
  

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efficient acquirer was the high bidder, so the outcome is assumed Pareto-efficient, yet theaftermarket found a mutual gain could arise from a transfer to an outbid rival with a lower
estimate of asset value. [ii] For both first-price and second-price auctions, 16% ofobservations found an inefficient acquirer submitting the high bid and then clicking on an
Accept Ask that exceeded all Accept Asks, including that selected by the efficient acquirer
whose estimate exceeded his.
While some variant of an endowment effect could lead to the second way in which
behavioral efficiency has been found distinct from Pareto efficiency, it bears notice that
distinction [i] is completely inconsistent with an endowment effect. More importantly, being
able to observe which auction outcomes are Pareto efficient and thus observe these
distinctions depends on having induced values and assumed motivational completeness andidentical risk tolerances. Using aftermarkets to observe the size and frequency of shortfalls
from behavioral efficiency requires none of these.
9. Readiness Remarks
These experiments used carefully designed aftermarkets to observe behavior yielding theinference of shortfalls from efficiency in 203 first-price auctions with a 28% frequency and$1.24 expectation, and in 142 second-price auctions with a 43% frequency and $1.79
expectation. Adding the aftermarket did not in these experiments affect bidding in theoriginal auction. While the experiments employed induced values, no aspect of induced
values was utilized in reaching these conclusions. A field study of a single-asset auction
could exactly mimic these procedures to obtain evidence on whether the efficient acquirer
won the auction and if not, the size of the inefficiency that arose, even in cases where
existence of equilibrium is in doubt (cf. Jackson [2009]) or equilibrium is incalculable.
The random-price procedure used when exactly one outbid bidder selected an Accept Bid
above the Accept Ask could directly be used to observe shortfalls from efficiency in bilateralbargaining over transfer of an indivisible asset or service. As pointed out in Harstad [2011],
the budget-balance feature of the aftermarkets reported here (that the amount theaftermarket purchaser paid is exactly the amount the aftermarket seller received) is notessential to appropriate aftermarket design. When field experiment budgets allow,
experimenters can provide incentives for field subjects to participate in aftermarkets bydesigning aftermarkets that run an experimenter-covered deficit. For example, in bilateralbargaining, efficiency conclusions could be drawn from an aftermarket design that, wheneverannouncements indicated a mutual gain, [a] paid the aftermarket seller 5% more than the
random price and charged the aftermarket buyer 5% less than the random price, or [b] paid
the aftermarket seller the Accept Bid and charged the aftermarket buyer the Accept Ask.
Fairly straightforward complications of the aftermarket design used here canaccommodate observing efficiency shortfalls for mechanisms seeking to allocate multiple
homogeneous assets. For example, following a mechanism for allocating two homogeneous
assets, potential buyers in an aftermarket could be asked for a pair of Accept Bids if seeking
to buy, an Accept ask if one asset won, or a pair of Accept Asks if two, with the rules thatwhenever an Accept Bid by a rival fell between an Accept Bid and a lower Accept Ask, it set
the price for that transaction, and a random price was consulted when necessary. It would
not matter whether bidders had single-unit or multi-unit demands. In larger, semicompetitive markets for homogeneous assets, a variant on a call market could serve as anaftermarket (so long as no trader were seeking both to buy more and to sell some of what he	  9had obtained), with the highest quantity where the demand price exceeded the supply pricetransacted, buyers paying the price of the last accepted supply unit, sellers receiving the(higher) price of the last accepted demand unit, and the experimenter covering the deficit.
In principle, aftermarkets could yield behavioral observations of shortfalls from efficiency
even in cases where public goods were being allocated, externalities arose, services had timedependent valuations, and/or packages of goods had synergistic values. It would still be thecase that a proper aftermarket design would require that the focal equilibrium of theallocation-mechanism-cum-aftermarket be focal equilibrium behavior in the allocation
mechanism followed by truthful revelation in the aftermarket. Exactly what constraints
these issues pose on aftermarket design is beyond the scope of this first demonstration.

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