Bribery an Favoritism by Auctioneers in Seale-Bi Auctions Roberto Burguet Institute for Economic Analysis (CSIC) an CREA Campus UAB Bellaterra, Barcelona, Spain 08193 Martin K. Perry * Department of Economics Rutgers University New Brunswick, New Jersey, USA 08901 First Draft: October 1999 Current Draft: April 2004 * Martin woul like to acknowlege te financial support of te Instituto e Analisis Economico (IAE, Institute for Economic Analysis) an te Institucio Catalana e Recerca i Estuis Avancats (ICREA, Catalan Institute for Researc an Avance Stuies) in Barcelona Spain. Roberto woul like to acknowlege financial support of FEDER an te Spanis Ministry of Science an Tecnology, projects SEC 2002-02506 an SEC 2003-08080- C02-02. In aition, we woul like to acknowlege Maria Lauve, Martin s researc assistant at Rutgers University, for er elp wit various computations an figures.
2 Abstract We consier bribery an favoritism in first-price procurement auctions. Te auctioneer can awar te contract to a isonest supplier at te low bi of an onest supplier. We examine te equilibrium biing functions of bot suppliers wen te isonest supplier can bribe te auctioneer. Bot efficient an inefficient bribes can arise an te resulting allocative istortion iffers from te istortions in a first-price auction or an optimal auction. Bribery as ambiguous effects on te aggressiveness of suppliers. Altoug bribery typically results in a iger expecte price for te buyer, tere are cases in wic te expecte price can be lower tan eiter a seconprice or first-price auction. JEL numbers: D44, L22, L14 Keywors: bribery, favoritism, auctions
3 1. Introuction Bribery is an illegal payment to a government official in return for a favor. 1 In tis paper, we will use te term bribery more broaly to escribe monetary sie-payments by a supplier to an auctioneer in orer to alter te awar of a procurement contract in favor of te supplier. Te auctioneer represents a buyer in te procurement of some goo. Te buyer coul be a government or a corporation, an te auctioneer woul be a procurement official or employee. Te awar of te contract in return for a payment coul take ifferent forms in ifferent contexts. In tis paper, we will analyze te excange between a corrupt auctioneer an a isonest supplier wereby te auctioneer allows te supplier to revise is bi, wen necessary to win te contract. Tat is, te auctioneer cannot awar te contract at a price above te low bi from te auction, but e can favor te isonest supplier by awaring im te contract at tat price. 2 Tis sceme inclues te special case of favoritism, were te auctioneer oes not receive any bribe in excange for awaring te contract. Tis specification of te auctioneer s iscretion in awaring te contract resembles some ocumente examples of bribery. For instance, Ingraam (2000) examines bribery in contracts aware by te New York City Scool Construction Autority uring te early 1990 s. Wen te bis were open publicly to awar te contract, te auctioneer save te bi from te bribing supplier until last an ten submitte a new bi for tis supplier just below te lowest bi of te oter suppliers. 3 More generally, tis paper provies some insigts into favoritism wit or witout bribes. Governments an corporations frequently ave a preference for particular suppliers of various goos. 1 Bribery as it anteceents in te practice of reciprocity in early civilizations. In a sense, reciprocity was a form of contract in wic a government official was expecte to perform some action in return for a payment. In early civilizations, reciprocity was te norm. Wit time, certain types of reciprocity became socially unacceptable an subject to penalties. Reciprocity first became unacceptable for juges, ten later became unacceptable for oter government officials. See Noonan (1984). See Rose-Ackerman (1999) for a general survey of corruption an potential solutions wit specific examples of bribery to government officials for procurement contracts in Capter 3. 2 Tus, te auctioneer can create a rigt of first refusal tat allows one supplier to resubmit a bi wic matces te lowest bi of te oter suppliers. 3 Lengwiler an Wolfstetter (2000) cite two major international construction projects (an airport in Berlin an a power station in Singapore) in wic bribes were pai to obtain te bis tat were submitte by te rivals..
4 Te goal of tis paper is to examine te effects of tis form of bribery or favoritism on te allocation of contracts an prices. We first examine ow bribery or favoritism affects te biing strategies of suppliers competing in a procurement auction. We ten ientify te effects of bribery on te allocation of contracts an te expecte price pai by te buyer. In Section 2, we present te moel were two suppliers compete in a first-price auction (FPA) to win a procurement contract, but one supplier is favore by te auctioneer. Te supplier wo is favore will be calle te isonest supplier (DS), an te oter supplier calle te onest supplier (HS). Te auctioneer emans a sare of te post-auction surplus efine as te ifference between te low bi of te HS an te cost of te DS, wenever tis ifference is positive. We call tis a sare bribe. Bribery or favoritism alters te biing strategies of bot suppliers. Te biing strategy of te HS will account for te fact tat te DS will be favore by te auctioneer. Te biing strategy of te DS will account for bot te opportunity an te cost of bribing te auctioneer. In Section 3, we caracterize tese equilibrium biing strategies an analyze ow te size of te sare bribe affects tis beavior. Altoug one migt conjecture tat bribery woul inuce te HS to bi more aggressively an te DS to bi less aggressively, we explain wy tis nee not be te case. In particular, wen te sare bribe receive by te auctioneer is large, te DS may bi more aggressively tan te HS, an also more aggressively tan e woul in te absence of corruption. In Section 4 we first analyze te allocative effects of bribery. We compare tis allocative istortion to tat wic arises in an asymmetric FPA witout bribery an an optimal auction. Bribery favors te allocation of te contract to te DS, weter e is ex ante stronger or weaker tan te HS in te sense of first orer stocastic ominance of te cost istribution. Tis contrasts wit bot te FPA an te optimal auction. Moreover, wit bribery, te allocative istortion is more pronounce for low cost realizations of te HS. Inee, te HS sets is bi to compete against te cost of te DS. Tus, te allocative istortions will be solely etermine by te biing beavior of te DS. Uner mil conitions, te lower te cost of te HS, te iger is bi is sae above is cost. In Section 5 we sow tat bribery may in fact result in a lower expecte price pai by te buyer, even toug te allocative istortions are not optimal an even toug te bribe pai to te auctioneer is a pure loss for te buyer. We illustrate tis result by analytically solving te
5 moel for a convenient family of cost istributions. Te expecte price will be lower tan eiter te expecte price in a FPA or in an efficient auction (suc as a secon-price auction (SPA)) wen te sare bribe is large an te HS is ex ante weaker tan te DS. Section 6 conclues an te iscussion of relate literature is presente in Appenix 1. 2. Te Moel of Bribery Te buyer as a value v for a goo wit a fixe quantity an quality. Te buyer employs an auctioneer to receive bis an awar a contract to purcase te goo from suppliers using a seale-bi first-price auction (FPA). In a fair auction witout bribery or favoritism, te contract woul be aware to te supplier wit te lowest bi at a price equal to tat bi. However, we examine an auction in wic te auctioneer can favor one of te suppliers. Te favore supplier will be calle te isonest supplier (DS) because e may nee to pay a bribe to te auctioneer. We assume tat tere is one oter supplier calle te onest supplier (HS). An important feature of our moel is tat te suppliers are asymmetric in tat tey ave ifferent istributions for teir costs of proucing te goo. We assume tat eac supplier raws is cost of prouction c i, were i = (DS) or (HS), from a istribution G i (c) wit a common support [0,1], an a positive ensity g i (c) over tis support. Te cost c i is private information for eac supplier, but te istribution functions are common knowlege. For simplicity, we also assume tat te value of te buyer excees te igest possible cost realization (v > 1). Finally, we assume tat te costs of te suppliers are inepenently istribute. Tus, we will examine bribery an favoritism in an asymmetric inepenent private value (cost) FPA. Te suppliers simultaneously bi for te contract, knowing teir cost, knowing te cost istribution of te oter supplier, an also knowing te form in wic bribery an favoritism occurs. Te auctioneer runs a seale-bi FPA an must awar te contract at a price equal to te lowest bi. However, te auctioneer nee not awar te contract to te supplier wo makes te lowest bi. If te bi of te DS is iger tan tat of te HS, te auctioneer can awar te contract to te DS at a price equal to te bi of te HS. In effect, te auctioneer allows te DS to
6 revise is bi ownwar in orer to matc a lower bi of te HS. 4 Let b an b, be te bis of te DS an te HS respectively. If b > b, te contract is aware to te DS at a price equal to is bi. However, if b > b, bribery or favoritism may occur. In particular, wen b > b > c, tere is surplus (b c ) wic can be ivie between te auctioneer an te DS. In tese cases, te auctioneer awars te contract to te DS at a price b, an te auctioneer receives a sare α [0,1] of te surplus (b c ). 5 We call α te sare bribe. Finally, if b > c > b, tere is no surplus tat te auctioneer an DS can sare, an te HS is aware te contract at a price equal to is bi. Te sare bribe α is etermine prior to te auction an tus is inepenent of te outcome of te auction. Te DS knows te value of α prior to submitting is bi. Te HS nee not know te value of α, but e knows tat te DS will be favore by te auctioneer an obtain te contract wenever b > c. Wen α = 0, te DS retains all of te surplus an no bribe is pai to te auctioneer. Tere are a number of interpretations for te sare bribe. First, te sare bribe coul be interprete as te relative bargaining power between te auctioneer an te DS in an efficient bargaining game. Uner tis interpretation, te auctioneer nees to infer te cost of te DS. However, tis inference nee not be mae before te assignment of te project. For instance, an inirect way to convey te necessary information is for te auctioneer to own a sare of te stock of te particular project, so tat auctioneer an DS nee only agree on teir sares of tat project. Also, te costs of te DS may be ex post verifiable from internal accounting recors or bi preparation ocuments. 6 4 One justification for restricting te price to be equal or below te bi of te HS is tat te price may become known at te en of te auction. Te HS wo was not aware te contract coul complain to te buyer if is bi were below te resulting price. In government procurement, te HS may be able to sue te government. 5 We assume tat any compensation to te auctioneer from te buyer is inepenent of te auctioneer s actions in awaring te contract, an tat tere are no punisments for accepting bribes. We are not attempting to moel te agency problem between te buyer an te auctioneer. Tere is a literature on tis topic. Krueger (1974) an Rose- Ackerman (1975, 1978) argue tat competition among bureaucrats woul reuce te bribes pai for government action. See also Rasmusen an Ramseyer (1994) for a game teoretic moel. Mookerjee an Png (1995) examine a moel in wic te buyer provies incentives wit compensation or punisment scemes to reuce bribery. 6 Wen DS as no creible way to inform te auctioneer about its cost (or te auctioneer as no creible way to inform te DS of te bi of HS), ten bargaining woul occur uner asymmetric information. In tis case, efficient bargaining is possible only in te extreme cases in wic α = 0 (favoritism).
7 3. Equilibrium Conitions for te Biing Functions In tis section, we caracterize te equilibria in a seale-bi FPA for te basic moel of bribery assuming general istribution functions for te costs of te two suppliers. Bribery will generally alter te equilibrium biing functions of bot suppliers. However, we fin tat bribery oes not make te equilibrium biing functions uniformly more or less aggressive for eiter supplier. In general, it is ifficult to solve for te equilibrium biing functions in an asymmetric FPA. Te asymmetric FPA becomes more tractable wit bribery. In particular, te game is ominance solvable. Once we exclue bis by te DS below is cost an exclue te rejection of contracts by te DS at a price above is cost, te HS as a ominant strategy against wic te DS can ten coose is biing strategy. Inee, te HS is effectively biing against cost of te DS because te DS will obtain te contract by winning outrigt or by bribing wenever is costs are below te bi of te HS. As a result, te biing strategy of te HS is inepenent of bot te biing strategy of te DS an te value of te sare bribe α. Te HS calculates is biing strategy by solving te following problem: (1) max Π [ b; c] = ( b c) [ 1 G ( b) ]. Te first-orer conition of tis problem is (2) [ G ( b) ] b 1 ( b c) g ( b) = 0. Te optimal biing function for te HS, b (c), is implicitly efine by (2). 7 Te DS s best response against te biing strategy of te HS is obtaine by solving te following problem: (3) max Π [ b; c, b ( ) ] = ( b c) [ 1 G ( b ( b)) ] + (1 ) ( b ( x) c) b 1 ( b 1 G ( x) ( c) 1 b ) α. b 7 Tis biing function is equivalent to te best take-it-or-leave-it offer tat a supplier wit cost c can make to a buyer wit a ranom valuation in te interval [0,1] given by te istribution function G. Te secon orer conitions require b [( 1 G( b)) / g( b)] to be increasing in b. We will assume tis conition ols for G i, i =,.
8 Te first term is te expecte profit wen te DS wins te auction outrigt witout bribery or favoritism. Te secon term is te expecte profit wen te DS loses te auction (b > b ), but bribes te auctioneer because is costs are below te bi of te HS (b > c). In tis case, te DS retains te sare (1 α) of te surplus (b - c). Te first-orer conition for tis problem is 1 1 b ( b) α. b (4) [ 1 G ( b ( b)) ] ( b c) g ( b ( b)) = 0 Te optimal biing function for te DS, b (c), is implicitly efine by (4). 8 Te effects of α on te biing beavior of bot suppliers are easy to caracterize. Proposition 1: Te biing function of te onest supplier, b (c) is inepenent of te sare bribe α. However, te biing function of te isonest supplier, b (c), sifts ownwar as te sare bribe increases. Proof: Te first result is obvious from inspection of te first-orer conition (2) efining b (c). Te secon result follows from ifferentiating te first-orer conition (4) wit respect to b an α: 1 b = α b 1 ( b) ( b c) g ( 1 ( )) b b b 2 π b 2 > 0, were 2 π b 2 is te erivative of te left an sie of (4) wit respect to b. Tis erivative is negative for interior solutions of (3). QED Te DS woul never bi below te minimum bi of te HS. Oterwise, te DS coul raise is bi witout reucing te probability of winning te auction outrigt. Tus, if te solution to (4) is below b (0), te DS simply bis b (0). At te igest cost realization, bot suppliers bi teir cost: b (1) = b (1) = 1. Wen α = 0, te DS bis unity for all cost realizations: b (c) = 1. Tus, wit favoritism, te DS oes not effectively bi for te contract, but is aware te contract wenever is cost is below te bi of te HS. On te oter an,
9 wen α < 1, te DS will bi to win te auction outrigt in orer to avoi paying te bribe: b (c) < 1 for all c < 1. It is easy to sow tat te DS prefers a smaller sare bribe. 9 We can now examine te effect of bribery on te biing strategies of te suppliers. Proposition 1 oes not fully answer tis question because no value of te sare bribe correspons to a fair auction witout bribery or favoritism. Even if α = 1, so tat te DS bribes te auctioneer witout saring in te surplus, an tus bis aggressively to win te contract, te HS still bis against te cost of te DS, an not against te bi of te DS. First, consier te first-orer conitions (2) an (4) for te symmetric case G = G. Te first term of eac conition is te incentive to raise te bi. Higer bis increase te profit on contracts tat te supplier wins outrigt in te auction. For a given cost realization common to bot suppliers, te first term in (2) for te HS is always less tan te corresponing term in (4) for te DS. Te secon term in te two first-orer conitions is te isincentive to raise te bi. Higer bis increase te probability of losing te auction an losing te corresponing profit on tose contracts. Te secon term for te DS is multiplie by α because te DS loses only te fraction α of te ifference between is bi an is cost on te contracts for wic is bi excees te bi of te HS. Tus, wen α < 1, te DS as a smaller isincentive to raise is bi, inucing im to bi less aggressively. Tese two forces suggest tat te DS bis less aggressively tan te HS. However, tere is an aitional factor in te secon term of te first-orer conition of te DS: 1 b ( b) / b. Tis factor is te slope of te inverse biing function of te HS. Wen te DS increases is bi marginally above b, tis factor is efine as te aitional cost realizations of te HS for wic te HS submitte a bi lower tan b. For tese contracts wic are no longer won outrigt, te DS losses te fraction α of te surplus wen e obtains tese contracts by a bribe. Tis factor 8 Tis assumes tat tis solution is interior on te range of bis [b (0),b (1)] of te HS. 9 For any given cost realization c an bi b, te profit function (3) of te DS is ecreasing in α. As a result, te envelope teorem implies tat a lower sare bribe will increase te expecte profits of te DS.
10 may well be greater tan unity, 10 in wic case te DS experiences a greater probability of losing te auction outrigt wen e increases is bi marginally. 11 Tus, tis factor increases te isincentive of te DS to raise is bi. Tis tir force works against te two previous forces, an is te reason wy tere is no general result tat te DS bis less aggressively tan te HS. We can also compare te biing function of te HS to te biing function of a supplier in a symmetric FPA witout bribery. Te first-orer conition for te biing function of it supplier witout bribery is G b 1 j b (6) [ 1 ( ( ))] ( ) ( ( )) = 0, j b c were j enotes te oter supplier. Comparing tis conition to te first-orer conition (2) for te HS, we see tat te same traeoffs apply. Te first term representing te incentive to raise te bi woul be larger witout bribery. However, te secon term representing te isincentive g j b 1 j b b 1 j b ( b) to raise te bi can also be larger because te factor 1 b ( b) / b may be greater tan 1. Tus, it is not clear tat favoritism towar te DS will cause te HS to bi more aggressively tan e woul in a FPA witout bribery. Figure 1 illustrates te equilibrium biing functions wit an witout bribery for te symmetric case wit G (c) = G (c) = c 2 for α = 1. Te ase line represents te biing function for a FPA witout bribery. Te soli lines represent te biing functions for te HS (ligter) an DS (arker). Wit bribery, te biing functions of te HS an te DS cross at a cost of approximately.55. Te HS bis more aggressively tan te DS at low cost realizations, but less aggressively at ig cost realizations. Tus, tere is no general result for wic te HS bis more (or less) aggressively tan te DS. Tis example also illustrates te effect of bribery on te biing of te HS. Te biing function of te HS wit bribery crosses is corresponing biing function in a FPA witout bribery at a cost of approximately.35. Te HS bis more 10 Tis factor will be greater tan unity wenever te margin between bi an cost of te HS, b (c) c, is ecreasing in c. For example, tis will be true wen g (c) is non-ecreasing in c. It will also be true for te family of cost istributions efine in Section 5. 11 Tis factor is also equivalent to te slope of te effective istribution of bis (costs) by te DS. In oter wors, it measures te fraction of aitional cost realizations of te DS tat woul obtain te contract (by biing or bribing) if te HS mae a similar marginal increase in is bi.
11 aggressively at low cost realizations, but less aggressively at ig cost realizations. Tus, tere is no general result in wic te HS bis more (or less) aggressively as a result of bribery. 4. Te Effect of Bribery on te Allocation of Contracts Wit bribery te allocation is inepenent of te DS s biing beavior, an te sare bribe. As suc, it is etermine solely by te biing function of te HS. Te biing function of te HS epens on te istribution of costs of te DS, G. A cange in G tat results in a new istribution tat stocastically ominates te original istribution makes te HS supplier bi more aggressively for low cost realizations. Tis reuces te expecte allocative istortion for any given a value of c. Wen te ifference between te bi an te cost of te HS supplier is smaller, it is less likely tat te cost of te DS c lies between te two. In fact, if te cange in te istribution also lowers te azar rate, a sligtly stronger conition, ten HS unambiguously bis more aggressively for any cost realization. Tus, we obtain te following proposition. Proposition 2: Given te cost realization of DS, te allocative istortion from bribery is iger for istributions of te DS wit lower inverse azar rate [ 1 G ( c) ] is inepenent of α. g ( c). Te allocative istortion Asymmetric FPAs generate allocative istortions because a supplier wo bis more aggressively will be aware te contract in some situations were is costs are iger tan te of te rival, will bi less aggressively. As a consequence, te allocative istortion in an asymmetric FPA witout bribery occurs by awaring te contract to te weaker supplier more often tan woul be efficient. 12 In contrast, an asymmetric FPA wit bribery allocates te contract to DS wenever te cost of te DS is below te bi of te HS. Since te HS bis above is cost, te FPA wit bribery istorts te allocation by awaring te contract to te DS more often tan woul be efficient. Tis occurs irrespective of weter te DS is stronger or weaker tan te HS. Wen te HS is stronger, a FPA wit or witout bribery favors te DS by allocating te contract to im in some cases wen e as iger costs. However, unlike a FPA witout bribery, 12 See Lebrun (1999) an Waerer (1999) for a more general examination of tis issue.
12 te allocative istortion in a FPA wit bribery oes not vanis as te costs of te suppliers approac te lowest possible realization. As in a FPA, an optimal mecanism favors allocating te contract to te weaker supplier. 13 Ten, once again, a FPA wit bribery istorts te allocation in te opposite irection from te optimal mecanism wen DS is te stronger supplier. Moreover, even wen te DS is te weaker supplier, te istortion wit bribery is very ifferent from te optimal istortion. Inee, in orer to reuce informational rents wit te lowest negative impact on efficiency, an optimal mecanism istorts te allocation in favor of te DS weaker supplier more at te iger cost realizations for te HS, wereas te istortion isappears wen approacing te lowest possible cost realization. In a precise sense, bribery istorts te allocation in te opposite way. Inee, if te cost istribution of te DS is caracterize by a monotone inverse azar rate, i.e., if [ 1 G ( c) ] g ( c) is ecreasing, ten te istance b ( c) c is ecreasing in c. Tis follows immeiately from (2). Tat is, b ( c) c is zero at c = 1, an attains te igest value at c = 0. Terefore, wen te cost of HS is close to 1, te HS wins te contract wenever it is efficient for im to win. However, wen te cost of te HS is close to 0, te DS wins te contract even wit a muc iger cost. 5. Te Effect of Bribery on te Expect Price Pai by te Buyer In tis section, we examine te effect of bribery on te expecte price. One migt expect tat te expecte price pai by te buyer woul increase wit bribery. First, bribery inuces non-optimal allocative istortions. Secon, te bribe payment to te auctioneer is a tax on te transaction. One migt also expect tese problems to be more acute wen te sare bribe pai to te buyer is iger. For several reasons, we will sow tat tese results nee not obtain. First, bribery may inuce te HS to bi more aggressively. Secon, from Proposition 1, te DS bis more aggressively wen te sare bribe is iger. In fact, we can sow tat Proposition 3: Te price expecte by te buyer is lower wen te sare bribe α is iger.
13 Proof: Notice tat te bi of te HS is inepenent of α. On te oter an, from our previous lemma b ( c) < 0 α for c < 1. Since te price pai by te buyer is simply min{ b, b }, we ave tat for any realization of te cost c, te expecte price is lower te lower α. QED. Now, if we consier again equations (2) an (3), we notice tat for α = 1, (4) is te same first-orer conition tat DS solves wen competing in a FPA witout bribery. Equation (2), on te oter an, is te biing function of a supplier competing against a virtual competitor tat bis cost. We know tat te HS nee not bi more aggressively. Even if te HS oes bi more aggressively, te DS nee not bi consistently more aggressively. However, one migt conjecture tat bot te HS an DS bi more aggressively, terefore causing te price expecte by te buyer to ecline. In orer to examine tis possibility, we efine te one-parameter family of istribution functions G(c;t) = 1 [1 c] t over te support [0,1] were c is te cost an t > 0 is a parameter wic can vary between te suppliers. 14 Te corresponing ensity function is g(c;t) = t [1 c] t 1. Te iger t, te iger is G(c;t) an te lower is [ 1 G ( c) ]. So iger t s imply g ( c) stronger suppliers in te sense of bot first orer stocastic an azar rate ominance. Let t efine te cost istribution of te HS an t efine te cost istribution of te DS, an enote G (c) = G(c;t ) an G (c) = G(c;t ). Te equilibrium biing function of te HS from (2) as te following linear form: 1 t (7) b ( c) = + c. 1+ t 1+ t Te equilibrium biing function of te DS from (4) is sligtly more complicate. It takes te following form: 13 See Myerson (1981), an McAfee an McMillan (1989).
14 1 α t (8) b ( c; α) = + c for c> c, 1+ α t 1+ α t 1 = 1 + t, for c c, α t t were c = max{0, }. Figure 2 epicts representative biing functions for te α t (1 + t ) suppliers for te two expressions of c in (8). Now we turn to te expecte price wit tis family of istributions. We first compare te expecte price in te FPA wit bribery to te expecte price tat woul arise wit an efficient auction, like te secon-price auction (SPA). 15 Let Ep α ; t, t ) be te expecte price in te ( FPA wit bribery, an Ep ( t, t ) be te expecte price in a SPA. 16 See Appenix 2 for te 2 expressions of tese expecte prices. Te following proposition provies comparisons of tese two expecte prices. Proposition 4: (i) Wen t > t, te expecte price in a FPA wit bribery can be below te expecte price in a SPA. In particular, tere exists a set of sare bribes ( α, 1 ] suc tat for any α in tis set, Ep ( t, t ) > Ep( α; t, t ). 2 (ii) Wen t t, te expecte price in a FPA wit bribery is above te expecte price in a SPA. In particular, Ep ( t, t ) Ep( α; t, t ) for all α 1, an 2 Ep ( t, t ) < Ep( α; t, t ) for t t or α < 1. 2 14 Waerer an Perry (1998) sow tat tis istribution function is not as restrictive as it migt seem. Distributions of tis form follow irectly from natural properties, particularly a property corresponing to constant returns to scale. 15 Witout bribery, te allocation of te contract virtually etermines te total surplus tat can be ivie between te buyer an te suppliers, an ow it is ivie. Tis is an implication of te Revenue Equivalence Teorem. See Myerson (1981). Tus, since a SPA allocates te contract to te lowest cost supplier, te expecte price in a SPA provies te natural reference point for te ivision of total surplus in any efficient auction. 16 A SPA cannot ave bribery in te form efine by Section 2 since te contract is aware at a price equal to te secon igest cost. Tus, tere woul be no surplus for te supplier losing te auction to split wit te auctioneer.
15 Te proof of Proposition 4 is containe in Appenix 2. Proposition 4 compares te asymmetric FPA wit bribery to a SPA wic as no allocative istortions. However, it woul also be interesting to compare te expecte prices in an FPA wit an witout bribery. Let Ep ( t, t ) 1 be te expecte price pai by te buyer in a FPA witout bribery. Tis comparison is straigtforwar for te symmetric case. Wen α < 1, Ep( α ; t, t) > Ep ( 1; t, t) = Ep ( t, ) = Ep ( t, ). For te asymmetric case, te comparison is more ifficult because te asymmetric FPA witout bribery oes not ave analytic solutions for te biing functions even wit tis family of istributions. Neverteless, using numerical computations, we can sow tat bribery may increase te price pai by te buyer in a FPA but, for α close to 1, it may also reuce tat price. Wen t = 4 an t = 1, te expecte price pai by te buyer is.4943 witout bribery. (see Marsall, Meurer, Ricar, an Stromquist, 1994). Alternatively, wit bribery an α = 1, te expecte price is.4958. Tus, bribery increases te expecte price pai by te buyer, even toug α = 1. However, wen t = 3 an t = 2, te expecte prices witout an wit bribery are.4125 an.4122, respectively. Tus, bribery reuces te expecte price. We can furter illustrate Proposition 4 using te Bicomp 2 program of Li an Riley (1999) to compute te asymmetric FPA witout bribery. Figure 3 illustrates te expecte price wit an witout bribery for values of te capacity parameters (t,t ) wit α = 1. Te expecte prices are equal along te iagonal, an te expecte price wit bribery is always greater wen t < t. However, wen t > t, te expecte price wit bribery is lower wen t is only somewat larger tan t. Te expecte price wit bribery is again iger in te lower rigt region were t > t. Te previous ata from Marsall et. al. (1994) are marke by asterisks. 1 t 2 t 6. Conclusion We ave examine te effects of bribery on te beavior of suppliers an te outcome of a FPA. In te particular form of bribery tat we ave consiere, one supplier bribes te auctioneer in orer to cange is bi wen tis is necessary to win te contract. We ave sown tat tis form of bribery nee not make te favore supplier bi less aggressively or te Tis woul not be te case if te suppliers expect te auctioneer to submit fictitious bis in orer to limit te surplus
16 isfavore supplier bi more aggressively. Bribery istorts te allocation of te contract. In cases were te favore supplier is te ex ante stronger, bribery reverses te istortion tat FPAs inuce. Tat is, bribery causes te contract be assigne to te favore, stronger supplier more often tan is efficient, instea of less often. Even wen te favore supplier is ex ante weaker, bribery alters te allocation of te contract in funamental ways. In particular, inefficient allocation of te contract to te weaker, favore supplier occurs wit ig probability even wen te cost of te stronger isfavore supplier is very low. For similar reasons, tese properties of te allocation in te FPA wit bribery contrast sarply to te allocation inuce by optimal (onest) mecanisms. Te effects of bribery on te expecte price expecte by te buyer are also subtle. Wen te auctioneer appropriates a large fraction of te surplus, te price for te buyer may in fact be lower tan in te absence of bribery. Tere are several questions tis analysis opens. Wen te fraction of surplus appropriate by te auctioneer (te size of te sare bribe) is zero, tis moel is simply a moel of favoritism. Moreover, te favore supplier may be a subsiiary. Tus, te moel is appropriate to stuy questions relate to vertical integration an long term contract arrangements wit special suppliers. 17 Once long term consierations are introuce, te moel also suggests questions relate to investment incentives for suppliers. We are presently working on some of tese questions. We expect to witness more researc along tese lines. of te winning supplier. See Rotkopt an Harsta (1985) for a moel of auctioneer ceating in tis fasion. 17 See Burguet an Perry (2003)
17 References Beck, Paul J. an Micael W. Maer, A Comparison of Bribery an Biing in Tin Markets, Economic Letters 20 (1986), 1-5. Burguet, Roberto an Yeon-Koo Ce, Competitive Procurement wit Corruption, Ran Journal of Economics 35-1 (2004), pp. 50-68 Burguet, Roberto an Martin Perry, Preferre Suppliers an Vertical Integration in Auction Markets mimeo, IAE an Rutgers University (2003). Celentani, M., an Ganuza, J.J., (2002) "Corruption an Competition in Procurement," European Economic Review, 46, 1273-1303. Compte, Olivier, Ariane Lambert-Mogiliansky, an Tierry Verbier, Corruption an Competition in Public Market Auctions, mimeo, CERAS-ENPC, France, January 2000. Ingraam, Allan, Testing for Ceating Between Biers an Auctioneers in Seale-Bi Auctions, mimeo, University of Marylan, December 2000. Krueger, Anne C., Te Political Economy of te Rent-Seeking Society, American Economic Review 64(3) (June 1974), 291-303. Laffont, Jean-Jacques an Jean Tirole, Auction Design an Favoritism, International Journal of Inustrial Organization 9 (1991), 9-42. Lebrun, Bernar, "First Price Auctions in te Asymmetric N Bier Case," International Economic Review 40 (1999), 125-142. Lengwiler, Yvan an Elmar Wolfstetter, Auctions an Corruption, CESifo Working Paper #401, CESifo, Munic, 2000. Li, Huagang an Jon G. Riley, Auction Coice, mimeo, University of California at Los Angeles, 1999. Lien, Donal H. D., A Note on Competitive Bribery Games, Economic Letters 22 (1986), 337-341. Lien, Donal H. D., Corruption an Allocation Efficiency, Journal of Development Economics 33 (1990), 153-164. Marsall, Robert C., Micael J. Meurer, Jean-Francois Ricar, an Walter Stromquist, "Numerical Analysis of Asymmetric First Price Auctions," Games an Economic Beavior 7 (1994), 193-220.
18 McAfee, R. Preston an Jon McMillan, "Government Procurement an International Trae," Journal of International Economics 26 (May 1989), 291-308. Menezes, Flavio M. an Paulo K. Monteiro, Corruption an te Coice of Auction Format, mimeo, Getulio Vargas Founation, Rio e Janeiro, Brazil, February 2000. Miyagiwa, Kaz, Oligopoly an Discriminatory Government Procurement Policy, American Economic Review 81(5) (December 1991), 1320-1328. Mookerjee, Dilip an I.P.L. Png, Corruptible Law Enforcers: How Tey Soul be Compensate?, Economic Journal 105(428) (January 1995), 145-159. Myerson, Roger B., "Optimal Auction Design," Matematics of Operations Researc 6 (1981), 58-73. Noonan, Jon T. Jr., Bribes (New York: MacMillan Publising Company, 1984). Rasmusen, Eric an Mark J. Ramseyer, Ceap Bribes an te Corruption Ban: A Coorination Game among Rational Legislators, Public Coice 78(3-4) (Marc 1994), 305-327. Rose-Ackerman, Susan, Te Economics of Corruption, Journal of Public Economics 4 (1975), 187-203. Rose-Ackerman, Susan. Corruption: A Stuy in Political Economy (New York: Acaemic Press, 1978). Rose-Ackerman, Susan. Corruption an Government: Causes, Consequences, an Reform (Cambrige, U.K., Cambrige University Press, 1999). Rotkopt, Micael an Ronal Harsta, Two Moels of Bi-Taker Ceating in Vickrey Auctions, Journal of Business 68 (1995), 257-267. Waerer, Keit, Asymmetric Private Values Auctions wit Application to Joint Biing an Mergers, International Journal of Inustrial Organization 17(3) (April 1999), 437-452. Waerer, Keit an Martin K. Perry, Te Effects of Mergers in Open Auction Markets, mimeo, Rutgers University an US Bureau of Labor Statistics, 1998.
19 Appenix 1: Relate Literature Menezes an Monteiro (2000) examine two alternative moels of bribery. In te first moel, te auctioneer can accept a fixe bribe from te winning bier in orer to reuce is bi an pay a price equal to te secon igest bi. In te secon moel, te auctioneer can accept a fixe bribe from te losing bier in orer to increase is bi an buy te goo at a price equal to te igest bi. Wit tis secon moel, an efficiency loss can arise wit te propose biing strategies for a common uniform istribution. If all te suppliers can collue in setting te price for te auction, a bribery auction to obtain te contract from te auctioneer will be equivalent to an onest procurement wit te auctioneer taking te place of te buyer. See Beck an Maer (1986) an Lien (1986). Lien (1990) examines a bribery auction wit a preetermine price an illustrates te efficiencies tat arise wen te auction favors one bier. More recently, Compte, Lambert-Mogiliansky, an Verier (2000) ave sown tat collusion in setting te price for te auction can actually be equilibrium beavior. Tey examine a procurement auction in wic te auctioneer iscloses te low bi an allows all suppliers to offer bribes in orer to revise teir bis. Te autors focus on te collusive equilibrium in wic all te suppliers initially bi te reservation price of te buyer an ten compete in bribes to te auctioneer in orer to obtain te contract. Tus, tis moel illustrates ow bribery can subvert te procurement auction an create a pure bribery auction. Lengwiler an Wolfstetter (2000) examine a symmetric traitional first-price auction in wic te igest bier can bribe te auctioneer to lower is bi to te secon igest bi. Te igest bier an te auctioneer ten sare te surplus, equal to te ifference in te bis minus expecte penalties. Te contract is always aware to te igest bier, but te price is ajuste ownwar. Tus, tis specification is equivalent to our secon variant in wic a supplier can bribe to increase te price receive for te contract. However, it lacks te caracteristic of te basic moel in wic a supplier can bribe to lower is bi an obtain te contract. Since te option to bribe is available to all biers, te autors argue tat te biers ave te same expecte payoff even toug tey submit iger bis to compete for te surplus. Witout te penalties, te expecte gain of te auctioneer is equivalent to te expecte loss of te seller.
20 Tus, te moel as te caracteristics of a bribery auction in wic te auctioneer sares in te expecte payoff of te seller. Wit only a price imension for te competition, it appears tat joint biing an bribing typically collapse into pure bribery auctions. Some recent papers introuce corruption in multiimensional auctions, were quality is also a criterion an te agent can manipulate te assessment (or te verification) of tis quality. Celentani an Ganuza (2002) assume te agent favors some ranomly, ex-post supplier by granting it te contract an allowing it to supply some minimum quality in excange for a bribe. Quality is tus compromise (by assumption). Tey are mainly intereste on ow te level of competition affects te level of corruption, an sow tat more competitiveness may in fact worsen te problem of corruption. Burguet an Ce (2004) also assume tat te buyer must rely on an expert tir party to assess te quality of te goos, but suppliers compete in bribe offers to be favore in tis assessment. Tey sow tat bribery may serve as a collusive evise. Quality may be compromise troug te selection of less efficient firms, wic nees not be against te interest of more efficient ones. However, wen te agent s ability to manipulate is small te only effect of corruption may be to lower te price to te buyer wit no quality istortion. See also Laffont an Tirole (1991). Finally, Ingraam (2000) as recently examine a ata set of auctions run by te New York City Scool Construction Autority from 1990-1997. Te investigations of bi rigging tat occurre uring tis perio reveale a form of bribery an favoritism similar to te basic moel of tis paper. Ingraam posits a moel in wic te isonest supplier reveals is cost to te auctioneer an te auctioneer submits a fictitious bi for te isonest supplier just below te low bi of te onest suppliers, assuming tis low bi is above te reveale cost of te isonest supplier. For te symmetric case, Ingraam solves for te biing function of te onest suppliers competing against one isonest supplier. Te empirical finings suggest tat biing beavior by te suppliers was ifferent for te auctions in wic tere was evience of bribery.
21 Appenix 2: Expecte Prices Using te biing functions from Section 5, we can calculate te expecte price pai by te buyer in te FPA wit bribery: (A1) Ep( α; t 1+ t + t t, t ) = (1 + t )(1 + t ) (1 + t )(1 + t 1+ t + t ) t t α t 1+ α t t 1+ for α t t (Case 1), (A2) Ep( α, t 1, t ) = (1 + t + ) (1 + t t )(1 + t t + t ) 1+ t t 1+ α t α t t for α t t (Case 2). Also, we can calculate te expecte price in a SPA: (A3) Ep ( 2 t, t 1+ t + t t t ) =. (1 + t )(1 + t ) (1 + t )(1 + t )(1 + t + t ) Proof of Proposition (4): (i) Wen t > t, expression (A1) for te expecte price applies over te entire range of te sare bribe of α 1. Tis expecte price is continuous an eclines as α increases over tis range. At α = 0, tis expecte price is clearly greater tan te expecte price uner a SPA from (A3). However, at α = 1, te conition tat t > t implies tat tis expecte price is lower tan te expecte price uner a SPA. Tus, tere exists an α suc tat for all α >α, bribery woul result in a lower expecte price. (ii) Wen t < t, expression (A1) for te expecte price applies only for α t /t. But uner te conition tat t < t, tis expecte price is greater tat te expecte price uner a SPA from (A3) at α = t /t, an tus for all α t /t. Wen t = t, expression (A1) applies for all α 1, excees te expecte price in a SPA for α < 1, an equals te expecte price in a SPA for α = 1. Q.E.D.
22 1 b(c).7 b(c) No Bribery b(c).5 0.35.55 1 c Figure 1: G(c) = c 2
23
24 b(c;0) b(c) 1 b(c;1/9) α b(c;1/3) b(c;1) c' Figure 2: Biing Functions t = 1 an t = 3 α = {0, 1/9, 1/3, 1} 1 c
25 8 t Ep > Ep 1 4 Ep < Ep 1 * (3,2) * (4,1) 3 4 5 6 7 Figure 3 Ep > Ep 1 8 t