On Bidding Markets:
The Role of Competition
(Job-Market Paper)
Abstract
This paper analyzes the e⁄ects of industrial concentration on bidding behavior and
hence, on the seller s expected proceeds. These e⁄ects are studied under the CIPI
model, an a¢ liated value set-up that nests a variety of valuation and information
environments. We formally decompose the revenue e⁄ects coming from less
competition into four types: a competition e⁄ect, an inference e⁄ect, a winner s curse
e⁄ect and a sampling e⁄ect. The properties of these e⁄ects are discussed and
conditions for (non)monotonicity of both the equilibrium bid and revenue are stated.
Our results suggest that it is more likely that the seller bene ts from less competition
in markets with more complete valuation and information structures.
Keywords: auctions, competition, a¢ liation, inference
JEL Classi cation: C62, D44, D82, L41
,1 Introduction
The typical concern about any illegal collusion practice (cartels) or legal collusion
arrangement (mergers or consortia) is that these practices reduce the number of
participants in the market and hence, lessen competition, negatively a⁄ecting both
the price and the bid-taker s revenue. Nevertheless, in the context of auctions and
bidding markets, this conventional wisdom applies only to the case of independent
private value settings, as it has been modelled theoretically and empirically
supported by abundant literature. 1 The simplicity of the valuation and information
environments analyzed by this literature makes collusion practices negatively a⁄ect
the intensity of competition, what has been called the competition e⁄ect.2
However, under a common value and/or a¢ liated signals model, the higher
concentration provoked by joint bidding leads to other e⁄ects that may counteract
the competition e⁄ect, and induce a more aggressive bidding behavior. These e⁄ects
can be grouped into three classes: a winner s curse e⁄ect, an inference e⁄ect and an
information pooling e⁄ect. First, the reduction in the number of bidders in a common
value environment permits alleviation of the winner s curse, because now defeating
fewer bidders makes the ex post overoptimism less likely. This implies that a higher
industrial concentration increases the expected value of the item conditional on
winning the auction, and in consequence, bidders are less conservative. 3 The
inference e⁄ect may arise from some a¢ liated information structures, and can be
present in both private and common value environments. 4In this case, the reduction
in the number of participants may increase the aggressiveness of the bidding
behavior. The reason for this is that, although winning is interpreted as information
that the intensity of the competition is lower than before the auction starts, this
perception is weakened when the winner faces fewer rivals. Finally, the information
pooling e⁄ect improves the precision of the bidder s value estimate because a
coalition of bidders can observe either a new signal or a larger amount of signals
with better stochastic properties than an individual bidder. This e⁄ect also allows the
1 For theoretical works on (legal) joint bidding under the independent private value setting, see
Waehrer [39], Waehrer and Perry [40], Froeb, Tschantz and Crooke [9], [37], and [10], and Dalkir,
Logan and Masson [6]. Theoretical analysis on bidding rings with private values are provided by
Robinson [35], Mailath and Zemsky [21], McAfee and McMillan [25], Marshall et al. [22], and
Pesendorfer [29]. Finally, most empirical literature on illegal collusion derives its estimation models
from a theoretical set-up with private values as well. Some papers along these lines are Hewitt,
McClave and Sibley [14], Porter and Zona [33], Pesendorfer [29], Lanzillotti [19], Scott [36], Porter and
Zona [32], Bajari and Ye [2], and Baldwin, Marshall and Richard [3].
2 Given some properties of bidding rings (e¢ ciency and the possibility of side payments), illegal
collusion and mergers have the same anticompetitive e⁄ects on auction markets if values are private
(see McAfee [24]).
3 Theoretical approaches that characterize the winner s curse e⁄ect include Bulow and Klemperer
[4] and Hendricks, Pinkse and Porter [11]. On the other hand, a number of recent papers provide
empirical evidence of this e⁄ect in several auction markets such as Hong and Shum [15], Hendricks,
Pinkse and Porter [11], and Athias and Nuæez [1].
4 The previous literature refers to this e⁄ect as the a¢ liation e⁄ect; see Pinkse and Tan [31], Hong
and Shum [15], and Hendricks, Pinkse and Porter [11].
1
,winner s curse correction on bids to mitigate, leading to more aggressive bidding
behavior.5
Therefore, all these e⁄ects go in the same direction and encourage more aggressive
bids when an auction market becomes more concentrated because of mergers or
other joint bidding arrangements. As these e⁄ects dominate the competition e⁄ect
plus the statistic e⁄ect produced by the overall reduction in the number of
participants (a sampling e⁄ect), the possibility for increasing the bid-taker s expected
revenue remains open. As a result, the standard viewpoint that less competition is
always undesirable can clearly become challenged.6
All of this underlines the importance of analyzing, in a valuation and information
setting which is as complete as possible, the e⁄ects of (legal) joint bidding practices.
As a starting point for this general objective, this paper studies the e⁄ects of a change
in the number of bidders on both the equilibrium bid strategy and the seller s
proceeds.7 Consequently, we abstract away from any information pooling type e⁄ect.
This implies that one can infer the other e⁄ects from the hypothetical exercise in
which bidders merger but the acquired bidder s information is not used by the
acquiring one. We then make this exercise equivalent, from a methodological point
of view, to the case in which the number of bidders decrease because some of them
do not attend some particular auction or because they leave the industry.
From the previous literature, a good point of departure for our analysis is provided
by Pinkse and Tan [31], who examine conditions under which the equilibrium bid is
monotonic increasing with respect to the number of bidders n in a¢ liated private-
value models of rst-price auctions. In particular, they show the existence of a large
class of such models in which the equilibrium bid function is indeed not strictly
increasing in n. Furthermore, they propose a decomposition of the bidding e⁄ects
into two parts: a competition e⁄ect and an a¢ liation e⁄ect. This latter e⁄ect is
precisely the source of the surprising nding of Pinkse and Tan in a private value
environment, and it can also be present in a common value setup. They illustrate
their results with the conditionally independent private value (CIPV) model, a special
case of the a¢ liated private value (APV) model in which bidders valuations are a¢
liated through a common random component, but they are independently
distributed given a realization of this common component. In this environment , the
winner never regrets its winning so that the winner curse e⁄ect has no bite.
Accordingly, it is clear that in order to also examine the winner s curse e⁄ect, we
need to consider a more general framework than that provided by the APV model -
5 See DeBrock and Smith [7], Hendricks and Porter [12], Krishna and Morgan [18]. Mares and Shor
[23] show that indeed this information pooling e⁄ect works unambiguously for secondprice auctions,
but for rst-price auctions it induces more aggressive bids only for signals that are su¢ ciently low.
6 In addition, it has been argued that joint bidding has other pros such as facilitating entry of
wealth-constrained bidders and improving risk diversi cation (see DeBrock and Smith [7]).
7 We do not examine the welfare e⁄ects of competition. For an analysis of such issues, see, for
instance, Compte and Jehiel [5].
2
, and in particular by the CIPV model -, as this e⁄ect cannot emerge from the valuation
structure characterized by these settings. One way to do this is by means of the
conditionally independent private information (CIPI) model, a special class of the
general a¢ liated value (AV) model which encompasses both the CIPV and the pure
common value setups as polar cases. In the CIPI model, the bidders signals (private
information) are a¢ liated through a common variable (which can also be the ex post
common value of the object), but they are independently distributed conditional on
a realization of this common variable. As a consequence, this framework provides an
environment rich enough to evaluate all the revenue e⁄ects.
We group the e⁄ects on revenue coming from more competition into two classes: (i)
those that a⁄ect bidding behavior and (ii) a pure sampling e⁄ect. On the one hand,
changes in the number of buyers in uence the equilibrium bid. As discussed above, in
environments with interdependent valuations and dependent information, bidding
behavior can become more or less aggressive with more competition. The nal sign of
these in uences on bids, as well as on revenues, is therefore ambiguous, and
depends on the relative magnitudes of the bidding-based e⁄ects considered. A more
in-depth characterization of these bidding e⁄ects can then become worthwhile for a
seller interested in adopting revenue-enhancing instruments in the face of mergers
or any joint bidding practice. Consequently, we propose a decomposition of this
bidding e⁄ect that allows us to isolate and formally evaluate the winner s curse, the
competition and the inference e⁄ects. The properties of all these e⁄ects are
established, and conditions for the (non)monotonicity of the equilibrium bid are
stated.
On the other hand, the sampling e⁄ect re ects the upward impact on the seller s
proceeds due to the fact that more competition implies a winning signal s
distribution with better stochastic properties. We then combine both the bidding
e⁄ect and the sampling e⁄ect, providing conditions for the (non)monotonicity of
revenues. In particular, the paper shows that the seller s expected proceeds can be
decreasing in the number of buyers as a negative and su¢ ciently large bidding e⁄ect
dominates the sampling e⁄ect. The main implication is that in the CIPI model, in
contrast to the CIPV setting, the conditions that allow the seller to bene t from less
competition are less stringent. The rationale of this nding is the presence of the
winner s curse e⁄ect, absent in a¢ liated private value environments. In fact, as the
winner s curse constitutes an additional force for bids decreasing in the number of
buyers, it makes the conditions for nonmontonic revenue to hold more likely. In a
broader sense, this work highlights therefore the role played by the valuation and
information structure assumed to be satis ed in a particular auction-based market.
Accordingly, our results suggest that, by analyzing a more complete auction
environment, the traditional idea that more concentration is always undesirable may
no longer hold.
Our model accounts for existing empirical evidence that, in auction markets in which
the winner s curse seems to be particularly strong, the bid-taker may be better o⁄
when the number of bidders decreases. For instance, DeBrock and Smith [7] study
3
The Role of Competition
(Job-Market Paper)
Abstract
This paper analyzes the e⁄ects of industrial concentration on bidding behavior and
hence, on the seller s expected proceeds. These e⁄ects are studied under the CIPI
model, an a¢ liated value set-up that nests a variety of valuation and information
environments. We formally decompose the revenue e⁄ects coming from less
competition into four types: a competition e⁄ect, an inference e⁄ect, a winner s curse
e⁄ect and a sampling e⁄ect. The properties of these e⁄ects are discussed and
conditions for (non)monotonicity of both the equilibrium bid and revenue are stated.
Our results suggest that it is more likely that the seller bene ts from less competition
in markets with more complete valuation and information structures.
Keywords: auctions, competition, a¢ liation, inference
JEL Classi cation: C62, D44, D82, L41
,1 Introduction
The typical concern about any illegal collusion practice (cartels) or legal collusion
arrangement (mergers or consortia) is that these practices reduce the number of
participants in the market and hence, lessen competition, negatively a⁄ecting both
the price and the bid-taker s revenue. Nevertheless, in the context of auctions and
bidding markets, this conventional wisdom applies only to the case of independent
private value settings, as it has been modelled theoretically and empirically
supported by abundant literature. 1 The simplicity of the valuation and information
environments analyzed by this literature makes collusion practices negatively a⁄ect
the intensity of competition, what has been called the competition e⁄ect.2
However, under a common value and/or a¢ liated signals model, the higher
concentration provoked by joint bidding leads to other e⁄ects that may counteract
the competition e⁄ect, and induce a more aggressive bidding behavior. These e⁄ects
can be grouped into three classes: a winner s curse e⁄ect, an inference e⁄ect and an
information pooling e⁄ect. First, the reduction in the number of bidders in a common
value environment permits alleviation of the winner s curse, because now defeating
fewer bidders makes the ex post overoptimism less likely. This implies that a higher
industrial concentration increases the expected value of the item conditional on
winning the auction, and in consequence, bidders are less conservative. 3 The
inference e⁄ect may arise from some a¢ liated information structures, and can be
present in both private and common value environments. 4In this case, the reduction
in the number of participants may increase the aggressiveness of the bidding
behavior. The reason for this is that, although winning is interpreted as information
that the intensity of the competition is lower than before the auction starts, this
perception is weakened when the winner faces fewer rivals. Finally, the information
pooling e⁄ect improves the precision of the bidder s value estimate because a
coalition of bidders can observe either a new signal or a larger amount of signals
with better stochastic properties than an individual bidder. This e⁄ect also allows the
1 For theoretical works on (legal) joint bidding under the independent private value setting, see
Waehrer [39], Waehrer and Perry [40], Froeb, Tschantz and Crooke [9], [37], and [10], and Dalkir,
Logan and Masson [6]. Theoretical analysis on bidding rings with private values are provided by
Robinson [35], Mailath and Zemsky [21], McAfee and McMillan [25], Marshall et al. [22], and
Pesendorfer [29]. Finally, most empirical literature on illegal collusion derives its estimation models
from a theoretical set-up with private values as well. Some papers along these lines are Hewitt,
McClave and Sibley [14], Porter and Zona [33], Pesendorfer [29], Lanzillotti [19], Scott [36], Porter and
Zona [32], Bajari and Ye [2], and Baldwin, Marshall and Richard [3].
2 Given some properties of bidding rings (e¢ ciency and the possibility of side payments), illegal
collusion and mergers have the same anticompetitive e⁄ects on auction markets if values are private
(see McAfee [24]).
3 Theoretical approaches that characterize the winner s curse e⁄ect include Bulow and Klemperer
[4] and Hendricks, Pinkse and Porter [11]. On the other hand, a number of recent papers provide
empirical evidence of this e⁄ect in several auction markets such as Hong and Shum [15], Hendricks,
Pinkse and Porter [11], and Athias and Nuæez [1].
4 The previous literature refers to this e⁄ect as the a¢ liation e⁄ect; see Pinkse and Tan [31], Hong
and Shum [15], and Hendricks, Pinkse and Porter [11].
1
,winner s curse correction on bids to mitigate, leading to more aggressive bidding
behavior.5
Therefore, all these e⁄ects go in the same direction and encourage more aggressive
bids when an auction market becomes more concentrated because of mergers or
other joint bidding arrangements. As these e⁄ects dominate the competition e⁄ect
plus the statistic e⁄ect produced by the overall reduction in the number of
participants (a sampling e⁄ect), the possibility for increasing the bid-taker s expected
revenue remains open. As a result, the standard viewpoint that less competition is
always undesirable can clearly become challenged.6
All of this underlines the importance of analyzing, in a valuation and information
setting which is as complete as possible, the e⁄ects of (legal) joint bidding practices.
As a starting point for this general objective, this paper studies the e⁄ects of a change
in the number of bidders on both the equilibrium bid strategy and the seller s
proceeds.7 Consequently, we abstract away from any information pooling type e⁄ect.
This implies that one can infer the other e⁄ects from the hypothetical exercise in
which bidders merger but the acquired bidder s information is not used by the
acquiring one. We then make this exercise equivalent, from a methodological point
of view, to the case in which the number of bidders decrease because some of them
do not attend some particular auction or because they leave the industry.
From the previous literature, a good point of departure for our analysis is provided
by Pinkse and Tan [31], who examine conditions under which the equilibrium bid is
monotonic increasing with respect to the number of bidders n in a¢ liated private-
value models of rst-price auctions. In particular, they show the existence of a large
class of such models in which the equilibrium bid function is indeed not strictly
increasing in n. Furthermore, they propose a decomposition of the bidding e⁄ects
into two parts: a competition e⁄ect and an a¢ liation e⁄ect. This latter e⁄ect is
precisely the source of the surprising nding of Pinkse and Tan in a private value
environment, and it can also be present in a common value setup. They illustrate
their results with the conditionally independent private value (CIPV) model, a special
case of the a¢ liated private value (APV) model in which bidders valuations are a¢
liated through a common random component, but they are independently
distributed given a realization of this common component. In this environment , the
winner never regrets its winning so that the winner curse e⁄ect has no bite.
Accordingly, it is clear that in order to also examine the winner s curse e⁄ect, we
need to consider a more general framework than that provided by the APV model -
5 See DeBrock and Smith [7], Hendricks and Porter [12], Krishna and Morgan [18]. Mares and Shor
[23] show that indeed this information pooling e⁄ect works unambiguously for secondprice auctions,
but for rst-price auctions it induces more aggressive bids only for signals that are su¢ ciently low.
6 In addition, it has been argued that joint bidding has other pros such as facilitating entry of
wealth-constrained bidders and improving risk diversi cation (see DeBrock and Smith [7]).
7 We do not examine the welfare e⁄ects of competition. For an analysis of such issues, see, for
instance, Compte and Jehiel [5].
2
, and in particular by the CIPV model -, as this e⁄ect cannot emerge from the valuation
structure characterized by these settings. One way to do this is by means of the
conditionally independent private information (CIPI) model, a special class of the
general a¢ liated value (AV) model which encompasses both the CIPV and the pure
common value setups as polar cases. In the CIPI model, the bidders signals (private
information) are a¢ liated through a common variable (which can also be the ex post
common value of the object), but they are independently distributed conditional on
a realization of this common variable. As a consequence, this framework provides an
environment rich enough to evaluate all the revenue e⁄ects.
We group the e⁄ects on revenue coming from more competition into two classes: (i)
those that a⁄ect bidding behavior and (ii) a pure sampling e⁄ect. On the one hand,
changes in the number of buyers in uence the equilibrium bid. As discussed above, in
environments with interdependent valuations and dependent information, bidding
behavior can become more or less aggressive with more competition. The nal sign of
these in uences on bids, as well as on revenues, is therefore ambiguous, and
depends on the relative magnitudes of the bidding-based e⁄ects considered. A more
in-depth characterization of these bidding e⁄ects can then become worthwhile for a
seller interested in adopting revenue-enhancing instruments in the face of mergers
or any joint bidding practice. Consequently, we propose a decomposition of this
bidding e⁄ect that allows us to isolate and formally evaluate the winner s curse, the
competition and the inference e⁄ects. The properties of all these e⁄ects are
established, and conditions for the (non)monotonicity of the equilibrium bid are
stated.
On the other hand, the sampling e⁄ect re ects the upward impact on the seller s
proceeds due to the fact that more competition implies a winning signal s
distribution with better stochastic properties. We then combine both the bidding
e⁄ect and the sampling e⁄ect, providing conditions for the (non)monotonicity of
revenues. In particular, the paper shows that the seller s expected proceeds can be
decreasing in the number of buyers as a negative and su¢ ciently large bidding e⁄ect
dominates the sampling e⁄ect. The main implication is that in the CIPI model, in
contrast to the CIPV setting, the conditions that allow the seller to bene t from less
competition are less stringent. The rationale of this nding is the presence of the
winner s curse e⁄ect, absent in a¢ liated private value environments. In fact, as the
winner s curse constitutes an additional force for bids decreasing in the number of
buyers, it makes the conditions for nonmontonic revenue to hold more likely. In a
broader sense, this work highlights therefore the role played by the valuation and
information structure assumed to be satis ed in a particular auction-based market.
Accordingly, our results suggest that, by analyzing a more complete auction
environment, the traditional idea that more concentration is always undesirable may
no longer hold.
Our model accounts for existing empirical evidence that, in auction markets in which
the winner s curse seems to be particularly strong, the bid-taker may be better o⁄
when the number of bidders decreases. For instance, DeBrock and Smith [7] study
3
