collusion in auctions and the role of communication to sustain it: a microeconomic approach

Collusion in auctions and the role of communication tosustain it : a microeconomic approach

Giuseppe Leonello

Barcelona Graduate School of Economics

July 7, 2014

Giuseppe Leonello (BGSE) Short title July 7, 2014 1 / 13

Overview

1 First SectionIntroduction

2 Second sectionLiterature review

3 Third sectionCollusion in second price auctions with endogenous choice ofcommunicate : an original microeconomic model


Introduction

”So prevalent are rings, in fact, that a retired auctioneer once noted thatin 40 years of auctioneering, he had yet to attend an auction at which aring was not present”. (Graham and Marshall 1987).


Introduction

Collusion in auctions is undesirable in the sense that it can decreasethe revenue obtained by seller

In the case of public procurement contracts the impact of thecollusion in auctions is even more harmful : The authorities want tobe sure they are getting good value for money

Bid rigging occurs when bidders agree among themselves to eliminatecompetition in the auction’s process, the most common practices are:

Bid suppression

Complementary bidding

Bid rotation (Possible in multiple objects or repeated auctions)


Literature review

Various authors have shown that environmental factors play a largerole in how profitable collusion can be (Skrzypacz and Hopenhayn,2004).

Not all bidding formats are equally immune to collusion.

Cartels are less profitable when facing a first-price auction than othercommon auction formats second-price auctions. (Marshall and Marx)

Second price auctions if specific conditions are satisfied leads toefficient collusion (Graham and Marshall)


Collusion in second price auction

In second price auction weakly dominant strategy to bid own good’s valuation

N bidders divided in two sub-groups , some of them are cartel members and the other areoutside the cartel

Efficient cartel : the object goes to the bidder in the cartel with highest valuation.

For the bidders outside the cartel the optimal strategy does not change : Bid theirvaluation.

Only the cartel member with highest valuation bid seriously while all the others bid zeroor a bid below the reserve price

If one cartel’s member has the highest valuation among all, the expected payments is reducedbecause it will compete only against the bidders outside the cartel

The ring profits will be shared among ring members through a transfert t

Self enforcing mechanism : Bidders in the ring not with the highest valuation to deviate andwin should bid more than their value.


Collusion in second price auctions with endogenous choiceof communicate

Second price auction leads to efficient collusion when bidders communicateand transfer moneyAssumption of perfect communication among bidders restrictive: cartelsare illegal and can be severely punished by the antitrust authority.

In this model the auctioneer can monitor the market and if communication amongbidders occurred, communicate the infringement to the antitrust and make invalidthe auction. In addition the ring members will be punished with an individual fine.

Bidders will decide if to collude taking into account the possibility to be punished.

Imperfect monitoring : The probability of discovering the communication amongbidders is function of the level of effort and it is costly.


The model

The framework of the model is the following

N = 2 Two bidders

Each bidder has two possible valuation of the good vi = vl , vh.

φ(e) probability of being discovered, if they collude, function of theauctioneer effort

c(e) cost of effort

F individual fine if discovered to collude

When bidders decide to colludeif different valuation, vh participate to the auction, the other bids the reserve price, andthen the winner will transfert a t to the other player.

If same valuation, the one participating to the auction will be choosen at random andthey will share the surplus


Collusive profits

The profits of bidder 1 will bewhen they collude

If vh,1, vl ,2 (vh − r − t)

If vl ,1, vh,2 t

If vh,1, vh,212 (vh − r)

If vl ,1, vl ,212 (vl − r)

When they do not collude

If vh,1, vl ,2 vh − vl

If vl ,1, vh,2 0

If they have the same valuation the winner will be choosen at random andwill pay the reserve price


The incentive constraint

Given the probability of being discovered and the expected profits with andwithout collusion, collusion will not arise if

[ 14 (vh − r − t) + 1

4(vh−r)

2 + 14

(vl−r)2 + 1

4 t][1 − φ(e)] − F [φ(e)] ≤

14 (vh − vl) + 1

4(vh−r)

2 + 14

(vl−r)2


The minimum level of effort

Solving for φ

φ ≥ 2(vl − r)

3vh + vl − 4r + 8F

The corresponding minimum effort will be

e∗ = φ−1(2(vl − r)

3vh + vl − 4r + 8F)

δφδvh

< 0 When the high value increases, taking constant everything else firms have less

incentive to collude because in a competitive setting, winning leads to higher profits.δφδvl

> 0 When the low value increases, taking constant everything else firms have more

incentive to collude because in the competitive setting, even if they win they will earn less.δφδF

< 0 When the Punishment increases there is less incentive to collude.


The choice of the auctioneer

If they collude, the expected profit for the auctioneer r and the c=0

If they do not collude, (the auctioneer has exerted the minimum required level of effort)

expected profits vl+r2

and c = c(e∗).

Then two possible equilibrium can arise.

c(e∗) ≤ vl + r

2− r

No communication in equilibrium ; e∗ = φ−1( 2(vl−r)3vh+vl−4r+8F )

c(e∗) >vl + r

2− r

Communication in equilibrium ; e∗ = 0


Recommendations

The auctioneer will not always exert the optimal level of effort since theexpected costs of doing it could be higher than the expected gains.COLLUSION IN EQUILIBRIUM

Possible government interventionThe minimum level of effort is a decreasing function of the punishment. Since increasingthe fine is not costly, one thing the government could do is to increase the punishment upto the maximum level.

Another possible solution, complementary to the maximum fine could be to subsidize theeffort that the auctioneer has to exert.

The government could subsidize the difference

c(e∗) − (vl + r

2− r)


collusion in auctions and the role of communication to sustain it: a microeconomic approach

Economy & Finance