The Impact of Subsidies in Asymmetric Procurement Auctions: A Comparison of Theoretical and Experimental Results

9th IFAC Conference on Manufacturing Modelling, Management and 9th IFAC Conference on Manufacturing Modelling, Management and 9th IFAC Conference on Manufacturing Modelling, Management and Control Available online at www.sciencedirect.com 9th IFAC Conference on Manufacturing Modelling, Management and Control Control 9th IFAC Conference on Manufacturing Modelling, Management and Berlin, Germany, August 28-30, 2019 Control 9th IFAC Conference on Manufacturing Modelling, Management and Berlin, Germany, August 28-30, 2019 Berlin, Control Berlin, Germany, Germany, August August 28-30, 28-30, 2019 2019 Control Berlin, Germany, August 28-30, 2019 Berlin, Germany, August 28-30, 2019

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IFAC PapersOnLine 52-13 (2019) 1990–1995

The Impact Subsidies in Asymmetric Procurement Auctions: The Impact of of Subsidies in Asymmetric Procurement Auctions: The of Subsidies in Asymmetric Procurement Auctions: TheAImpact Impact of Subsidies in Asymmetric Procurement Auctions: Comparison of Theoretical and Experimental Results The Impact of Subsidies in Asymmetric Procurement Auctions: AImpact Comparison of Theoretical Theoretical and Experimental Experimental Results TheA of Subsidies in Asymmetric Procurement Auctions: Comparison of and Results A Comparison of Theoretical and Experimental Results A Comparison of Theoretical and Experimental Results A Comparison of Theoretical andTim Experimental Results Sanghoon Fry, Sanghoon Cho, Cho, Joan Joan Donohue, Donohue, Tim Fry, Joel Joel Wooten Wooten

Sanghoon Sanghoon Cho, Cho, Joan Joan Donohue, Donohue, Tim Tim Fry, Fry, Joel Joel Wooten Wooten Sanghoon Cho, Joan Donohue, Tim Fry, Joel Sanghoon Cho, Joan Donohue, Tim Fry, Joel Wooten Wooten Moore School of Business, University of South Carolina, Columbia, South Carolina 29208 USA (e-mail: Moore School of Business, University of South Carolina, Columbia, South Carolina 29208 USA (e-mail: Moore School of Business, University of South Carolina, Columbia, South Carolina 29208 USA (e-mail: Moore School of Business, University of South Carolina, Columbia, South Carolina 29208 USA (e-mail: [email protected], [email protected], [email protected], [email protected]). [email protected], [email protected], [email protected], [email protected]). Moore School of Business, University of South Carolina, Columbia, South Carolina 29208 USA [email protected], [email protected], [email protected], [email protected]). Moore School of Business, University of South Carolina, [email protected], Columbia, South Carolina 29208 USA (e-mail: (e-mail: [email protected], [email protected], [email protected]). [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]). [email protected]). Abstract: The The existence existence of of discriminatory discriminatory auctions auctions where where one one class class of of bidders bidders is is offered offered preferential preferential Abstract: Abstract: The existence of discriminatory auctions where one class of bidders is offered preferential Abstract: The existence of discriminatory auctions where one class of bidders is offered preferential treatment over another class is controversial. Consider the Affirmative Action policies of the FCC and the the treatment over another class is controversial. Consider the Affirmative Action policies of the FCC and Abstract: The existence of discriminatory auctions where one class of bidders is offered preferential treatment over another class is controversial. Consider the Affirmative Action policies of the FCC and Abstract: The existence of discriminatory auctions where one class of bidders is offered preferential treatment over another class is controversial. Consider the Affirmative Action policies of the FCC and the the Buy-American Act Act policies policies of of the the US US Government. Government. The The political political reasons reasons for for such such policies policies are are obvious. obvious. Buy-American treatment over another class is controversial. Consider the Affirmative Action policies of the FCC and the Buy-American Act policies of the US Government. The political reasons for such policies are obvious. treatment over another class is controversial. Consider the Affirmative Action policies of the FCC and the Buy-American Act policies of the US Government. The political reasons for such policies are obvious. However, research has shown that there is an economic benefit for such policies in the sense that However, research has shown that there is an benefit for such policies in sense that Buy-American Act policies of the Government. The political for such policies are obvious. However, has shown that there isdecrease an economic economic benefitreasons for offered such policies in the the sense Buy-American Act to of may the US Government. The political reasons for policies such policies aresense obvious. However, research research has shown thatUS there is an economic benefit for such in the that procurement costs topolicies a buyer buyer may actually as incentives incentives are to weaker weaker sellers. In that this procurement costs a actually decrease as are offered to sellers. In this However, research has shown that there is an economic benefit for such policies in the sense that procurement costs to aa buyer may actually decrease as incentives are offered to weaker sellers. In this However, research has shown that there is an economic benefit for such policies in the sense that procurement costs to buyer may actually decrease as incentives are offered to weaker sellers. In this paper, we test the predictions of Rothkopf et al. (2003) where cost weaker sellers are offered a subsidy in paper, we test the predictions of Rothkopf et al. (2003) where cost weaker sellers are offered aa subsidy in procurement costs to a buyer may actually decrease as incentives are offered to weaker sellers. In this paper, we test the predictions of Rothkopf et al. (2003) where cost weaker sellers are offered subsidy in procurement costs to a buyer may actually decrease as incentives are offered to weaker sellers. In this paper, we test the predictions of Rothkopf et al. (2003) where cost weaker sellers are offered a subsidy in the form of additional payment. For various levels of cost disadvantage, Rothkopf et al (2003), present the the form of additional payment. For various levels of cost disadvantage, Rothkopf et al (2003), present the paper, we test the predictions of Rothkopf et al. (2003) where cost weaker sellers are offered a subsidy in the form of additional payment. For various levels of cost disadvantage, Rothkopf et al (2003), present the paper, we test the predictions of Rothkopf et al. (2003) where cost weaker sellers are offered a subsidy in the form of additional payment. For various levels of cost disadvantage, Rothkopf et al (2003), present the optimal subsidy level, bidders' strategies, bidder profitability, and buyer procurement costs. We test these optimal subsidy level, payment. bidders' strategies, bidder profitability, and buyer Rothkopf procurement costs. We test these the form of For levels of cost et (2003), the optimal bidders' strategies, bidder and procurement We test these the formsubsidy of additional additional For various various levelsprofitability, ofThis cost disadvantage, disadvantage, Rothkopf et al alcosts. (2003), present the optimal subsidy level, bidders' strategies, bidder profitability, andis buyer procurement costs. Wepresent test these predictions in aa level, seriespayment. of controlled controlled experiments. This paper isbuyer the first first to experimentally experimentally test these predictions in series of experiments. paper the to test optimal subsidy level, bidders' strategies, bidder profitability, and buyer procurement costs. We test these predictions in a level, series of controlled experiments. Thistopaper is the first to experimentally test optimal subsidy bidders' strategies, bidder profitability, and buyer procurement costs. We test predictions in a series of controlled experiments. This paper is the first to experimentally test these predictions. Due to the wide use of subsidies not only support social aims but also their potential to predictions. Due to the wide use of subsidies not only topaper support social aims but also their potential to predictions in aa series controlled experiments. This is first to experimentally test these predictions. Due to the wide use of not only support social aims also their to predictions in series of controlled experiments. Thisto is the the first to but experimentally test predictions. Due to costs, the of wide use of subsidies subsidies not financial only topaper support social aims but alsoCopyright their potential potential to reduce the the buyer's buyer's costs, our findings have both both financial and societal societal implications. Copyright © these 2019 reduce our findings have and implications. © 2019 predictions. Due to the wide use of subsidies not only to support social aims but also their potential to reduce the buyer's costs, our findings have both financial and societal implications. Copyright © 2019 predictions. Due to the wide use of subsidies not only to support social aims but also their potential to reduce the buyer's costs, our findings have both financial and societal implications. Copyright © 2019 IFAC IFAC reduce buyer's costs, findings both societal implications. © IFAC © 2019,the IFAC (International Federation Automatic Control) and Hosting by Elsevier Ltd. All Copyright rights reserved. reduce the buyer's costs, our our findings ofhave have both financial financial and societal implications. Copyright © 2019 2019 IFAC IFAC Keywords: procurement auction; subsidies; private values; asymmetric sellers; behavioral operations IFAC Keywords: procurement auction; subsidies; private values; asymmetric sellers; behavioral operations Keywords: Keywords: procurement procurement auction; auction; subsidies; subsidies; private private values; values; asymmetric asymmetric sellers; sellers; behavioral behavioral operations operations management management Keywords: procurement auction; subsidies; private values; asymmetric sellers; behavioral management Keywords: operations managementprocurement auction; subsidies; private values; asymmetric sellers; behavioral operations management management Aside from the the political political and and social social benefits Aside from benefits resulting resulting from from 1. INTRODUCTION Aside from the political and social benefits resulting from 1. INTRODUCTION Aside from the political and social benefits resulting from such auctions, research has shown that when bidders are 1. such auctions, research has shown that when bidders are in in 1. INTRODUCTION INTRODUCTION Aside from the political and social benefits resulting from such auctions, research has shown that when bidders are Aside from the political and social benefits resulting from such auctions, research has shown that when bidders are in in some way different such that one class of bidders is There are many situations where a purchasing agent in a 1. INTRODUCTION some way different such that one class of bidders is There are many situations where a purchasing agent in a 1. INTRODUCTION such auctions, research has shown that when bidders are in some way different such that one class of bidders is There are many situations where aa purchasing agent in aa such auctions, research has shown that when bidders are in some way different such that one class of bidders is There are many situations where purchasing agent in disadvantaged compared to another, the optimal auction procurement auction, especially in the public sector, may disadvantaged compared to another, another, theofoptimal optimal auction procurement auction, especially ina purchasing the public public sector, sector, may some way different such one class bidders is There are many situations where agent in aa disadvantaged compared to the auction procurement auction, especially the may some way different such that that onein class bidders is class disadvantaged compared to another, theofoptimal auction There are many situations wherein a purchasing agentof in procurement auction, especially in theanother public sector, may design is one that discriminates favor of the weaker want to favor one type of bidder over type bidder. design is one that discriminates in favor of the weaker class of of want to favor one type of bidder over another type of bidder. disadvantaged compared to another, the optimal auction procurement auction, especially in the public sector, may design is one that discriminates in favor of the weaker class want to favor one type of bidder over another type of bidder. disadvantaged compared to another, the optimal auction design is one that discriminates in favor of the weaker class of of procurement auction, especially in the public sector, may want to favor one type of bidder over another type of bidder. bidders (Myerson, 1981). Despite being inefficient in the For example, the agent may want to favor a particular type of bidders (Myerson, 1981). Despite being inefficient in the For example, the agent may want to favor a particular type of design is one that discriminates in favor of the weaker class of want to favor one type of bidder over another type of bidder. bidders (Myerson, 1981). Despite being inefficient in the For example, the agent may want to favor a particular type of design is one that discriminates in favor of the weaker class of bidders (Myerson, 1981). Despite being inefficient in the want to favor one type of bidder over another type of bidder. For example, the agent may want to favor a particular type of sense that a procurement auction may be won by a seller with bidder based minority ownership, size business, sense that procurement auction may beinefficient won by by aa seller seller with bidder based on on minority ownership, size of of business, or or bidders (Myerson, 1981).auction Despite being in the For example, the agent may want aa particular type sense aaa procurement may be won with bidder based on ownership, size business, or bidders (Myerson, Despite being in theshown sense that that procurement auction may beinefficient won by a seller with For example, theminority agent may want to toaa favor favor particular type of of bidder based on minority ownership, size of of business, or higher costs over aa 1981). seller with lower costs, research has whether the business is considered domestic or foreign higher costs over seller with lower costs, research has shown whether the business is considered domestic or foreign sense that aa procurement auction may be won by aa seller with bidder based on minority ownership, size of business, or higher costs over aa seller with lower costs, research has shown whether the business is considered aa reason domestic or foreign sense that procurement auction may be won by seller with higher costs over seller with lower costs, research has shown bidder based on minority ownership, size of business, or whether the business is considered domestic or foreign that total procurement costs to the buyer may actually be supplier. Undoubtedly, the principal why one type of that total procurement costs to lower the buyer buyer may actually beshown supplier. Undoubtedly, the principala reason reason why one type of of higher costs over with costs, research has whether the business is considered domestic or foreign that procurement costs to the may actually supplier. Undoubtedly, principal why type higher costs over aa seller seller with costs, research hasbe that total total procurement costs to lower the buyer may actually beshown whether the business is the considered a reason domestic or one foreign supplier. Undoubtedly, the principal why one type of reduced by offering incentives to weaker types of sellers bidder would be favored over another in aa procurement reduced by offering incentives to weaker types of sellers bidder would be favored over another in procurement that total procurement costs to the buyer may actually be supplier. Undoubtedly, the principal reason why one type of reduced by offering incentives to weaker types of sellers bidder would be favored over another in aacorrect procurement that total procurement costs to the buyer may actually be reduced by offering incentives to weaker types of sellers supplier. Undoubtedly, the principal reason why one type of bidder would be favored over another in procurement (Ayers and Cramton, 1996; Corns and Schotter, 1999; auction is for political purposes: trying to for past (Ayers and Cramton,incentives 1996; Corns Corns and Schotter, Schotter, 1999; auction is for for political political purposes: tryinginto to correct for past past reduced by to weaker types sellers bidder be favored over procurement (Ayers Cramton, 1996; and auction is purposes: trying for reduced by offering offering incentives to and weaker types of of1999; sellers (Ayers and and Cramton, 1996; Corns andMcMillan, Schotter, 1999; bidder would becase favored over another another intoaacorrect procurement auctionwould is in forthe political purposes: trying correct forto past Hellerstein, et al., 2011; McAfee 1989; injustices of minority ownership; trying protect Hellerstein, et al., 2011; McAfee and McMillan, 1989; injustices in the case of minority ownership; trying to protect (Ayers and Cramton, 1996; Corns and Schotter, 1999; auction is for political purposes: trying to correct for past Hellerstein, et al., 2011; McAfee and McMillan, 1989; injustices in the case of minority ownership; trying to protect (Ayers and Cramton, 1996; Corns and Schotter, 1999; Hellerstein, et al., 2011; McAfee and McMillan, 1989; auction is for political purposes: trying to correct for past injustices in the case of minority ownership; trying to protect Myerson, 1981; Rothkopf, et al., 2003). The reason for small businesses against large businesses; and trying to Myerson, 1981; Rothkopf, et al., al., 2003). 2003). The reason reason for this this small businesses against large businesses; businesses; andtrying tryingtoto toprotect Hellerstein, et al., 2011; McAfee and McMillan, 1989; injustices in the case of minority ownership; Myerson, 1981; Rothkopf, et The for this small businesses against large and trying Hellerstein, et al., 2011; McAfee and McMillan, 1989; Myerson, 1981; Rothkopf, et al., 2003). The reason for by thisthe injustices in the case of minority ownership; trying to protect small businesses against large businesses; and trying to unexpected result is that the level of competition faced protect domestic suppliers against foreign suppliers. Consider unexpected resultRothkopf, is that that the theetlevel level of competition competition faced by the protect domestic suppliers suppliers against foreign suppliers. suppliers. Consider Myerson, 1981; al., 2003). The reason for this small businesses against large businesses; and trying to unexpected result is of faced by the protect domestic against foreign Consider Myerson, 1981; Rothkopf, et al., 2003). The reason for this unexpected result is that the level of competition faced by the small businesses against large businesses; and trying to protect domestic suppliers against foreign suppliers. Consider stronger and weaker bidders differs. Suppose there are five the Buy-American Act the government offers aa stronger andresult weaker bidders differs. Suppose there are five five the Buy-American Act where where the US US government offers unexpected is that the level of competition faced by the protect domestic suppliers against foreign suppliers. Consider stronger and weaker bidders differs. Suppose there are the Buy-American Act where the US government offers a unexpected result is that the level of competition faced by the stronger and weaker bidders differs. Suppose there are five protect domestic suppliers against foreign suppliers. Consider the Buy-American Act where the US government offers a weaker firms and five stronger firms competing in a small business supplier a 12 percent preference over a large weaker firms and five five stronger stronger firmsSuppose competing in aaare five small business supplier supplier 12 percent percent preference over large stronger and differs. there the Buy-American Act where the US government offers aa weaker firms and firms competing in small business aaa 12 over aaa large stronger and weaker weaker bidders differs. Suppose there five the weaker firms and fivebidders stronger firmsfirms competing in aare the Buy-American Actbid where USpreference government offers small business supplier 12 percent preference over large procurement auction. While weaker compete against supplier: if the lowest by aathe small business is no more than procurement auction. While weaker firms compete against the supplier: if the lowest bid by small business is no more than weaker firms and five stronger firms competing in aaagainst small business supplier aa 12 percent preference over aa large procurement auction. While weaker firms compete the supplier: if the lowest bid by aaasmall business is no more than weaker firms and five stronger firms competing in procurement auction. While weaker firms compete against the small business supplier 12 percent preference over large supplier: if the lowest bid by small business is no more than other four weaker firms and five stronger firms, stronger firms 12 percent higher than that of large business, the contract is other four weaker firms and five stronger firms, stronger firms 12 percent higher than that of a large business, the contract is procurement auction. While weaker firms compete against the supplier: if the lowest bid by aaaasmall business is no more than other four weaker firms and five stronger firms, stronger firms 12 percent higher than that of large business, the contract is procurement auction. While weaker firms compete against the other four weaker firms and five stronger firms, stronger firms supplier: if the lowest bid by small business is no more than 12 percent higher than that of large business, the contract is compete against the other four stronger firms and five weaker awarded to small business (Manuel, 2016). For Federal compete against the other four stronger firms andstronger five weaker weaker awarded to higher the small small business (Manuel, 2016). the Forcontract Federal is other four weaker firms and five stronger firms, firms 12 percent than that of large compete against other four stronger firms and five awarded to the 2016). For Federal other four weaker firms and five stronger firms, firms compete against the other four stronger firms andstronger five weaker 12 percent thanbusiness thatpreference of aa(Manuel, large business, business, the is awarded to higher the small business (Manuel, 2016). Forcontract Federal firms. The resultsthe are that the stronger firms face less government contracts, the for aa domestic supplier firms. The results are that the stronger firms face less government contracts, the preference for domestic supplier compete against the other four stronger firms and five weaker awarded to the small business (Manuel, 2016). For Federal firms. The results are that the stronger firms face less government contracts, the preference for a domestic supplier compete against the other four stronger firms and five weaker firms. The results are that the stronger firms face less awarded to the small business (Manuel, 2016). For Federal government contracts, the preference for a domestic supplier competition compared to the weaker firms. However, by competing against a foreign supplier is 6 percent and 50 competition compared to the the weaker firms. However, by competing against foreign supplier is isfor66 apercent percent andsupplier 50 firms. The results are that the stronger firms face government contracts, the preference domestic competition compared to firms. However, by competing against aaa foreign supplier and 50 firms. The results are theweaker stronger firms face less less competition compared to the weaker firms. However, bylike government theof preference for6 apercent domestic competing against foreign supplier is andsupplier 50 incentives to weaker firms, they become more percent for aacontracts, Department Defense (DOD) supplier. Another offering incentives to that weaker firms, they become moreby like aaa percent for against Department of Defense (DOD) supplier. Another offering competition compared to the weaker firms. However, competing a foreign supplier is 6 percent and 50 offering incentives to weaker firms, they become more like percent for a Department of Defense (DOD) supplier. Another competition compared to the weaker firms. However, by offering incentives to weaker firms, they become more like a competing against a foreign supplier is 6 percent and 50 percent for a Department of Defense (DOD) supplier. Another stronger firm. The increase in in competition results in the well-known example of preferential treatment was the 1993 stronger firm. The increase in in competition results in the well-known example of preferential treatment was the 1993 offering incentives to weaker firms, they become more like aa percent for aaexample Department of Defense (DOD) supplier. Another stronger firm. The increase in in competition results in the well-known of preferential treatment was the 1993 offering incentives to weaker firms, they become more like stronger firm. The increase in in competition results in the percent for Department of Defense (DOD) supplier. Another well-known example of preferential treatment was the 1993 firms bidding more aggressively. While incentives Federal Communications Commission (FCC) auctions for stronger firm. firms The bidding moreinaggressively. aggressively. While incentives Federal Communications Commission (FCC) auctions auctions for stronger increase in competition results in the well-known example of preferential treatment was the 1993 firms bidding more While incentives Federal Communications Commission (FCC) for stronger firm. increase inbid competition results in firms bidding moreinto aggressively. While incentives well-known example preferential was the 1993 Federal Communications Commission (FCC) auctions for The cause the weaker firms less if proper slices of regional radio (Ayers and Cramton, 1996). may cause the The weaker firms to bid less aggressively, aggressively, if the proper slices ofCommunications regional radioofbands bands (Ayerstreatment and Cramton, 1996). The may stronger firms bidding more aggressively. While incentives Federal Commission (FCC) auctions for may cause the weaker firms to bid less aggressively, if proper slices of regional radio bands (Ayers and Cramton, 1996). The stronger firms bidding more aggressively. While incentives may cause the weaker firms to bid less aggressively, if proper Federal Communications Commission (FCC) auctions for slices of regional radio bands (Ayers and Cramton, 1996). The incentives are used, the increase in aggressive bidding by the intent the FCC auctions was to ensure that minority-owned incentives are used, the increase in aggressive bidding by the intent of the FCC auctions was to ensure that minority-owned may cause the weaker firms to bid less aggressively, if proper slices of regional radio bands (Ayers and Cramton, 1996). The incentives are used, the increase in aggressive bidding by the intent the FCC auctions was to ensure that minority-owned may cause the weaker firms to bid less aggressively, if proper incentives are used, the increase in aggressive bidding by the slices of regional radio bands (Ayers and Cramton, 1996). The intent the FCC auctions was to ensure that minority-owned stronger firms will more than compensate for the reduced businesses were given the opportunity to compete for these stronger firms will more more than compensate compensate for the the reduced businesses were given the opportunity opportunity to that compete for these these incentives are used, the increase in aggressive bidding by the intent of the FCC auctions was to ensure minority-owned stronger firms will than for reduced businesses were given the to compete for incentives are used, the increase in aggressive bidding by the stronger firms will more than compensate for the reduced intent of the FCC auctions was to ensure that minority-owned businesses were given the opportunity to compete for these aggressive bidding by the weaker firm which, overall, results radio bands such that minority buyers were given favorable aggressive bidding by the the weaker weaker firm which, which, overall, results radio bandswere suchgiven that minority minority buyers were were given favorable favorable stronger firms will more compensate for reduced businesses the opportunity to for aggressive bidding by firm overall, results radio such that buyers given stronger firms willbuyer. more than compensate for the the reduced aggressive bidding by thethan weaker firm which, overall, results businesses were thesome opportunity to compete compete for these thesein radio bands bands suchgiven that minority buyerswere were givenaa favorable in less cost to the financing options and in cases given discount in in less cost to the buyer. financing options and in some cases were given discount aggressive bidding by the weaker firm which, overall, radio bands such that minority buyers were given favorable in less cost to the buyer. financing options and in some cases were given aa favorable discount in aggressive bidding by the weaker firm which, overall, results results in less cost to the buyer. radio bands such that minority buyers were given financing options and in some cases were given discount in the form of a 40 percent credit. the form of of aa 40 40 percent credit. in financing and some the in less less cost cost to to the the buyer. buyer. financing options and in in credit. some cases cases were were given given aa discount discount in in the form form ofoptions a 40 percent percent credit. the form of a 40 percent credit. the form of a 40 percent credit. 2405-8963 © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. 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While the type of preference mechanism to be used depends on the intent of the buyer and the economic situations in play, determining the exact level of incentive to be set under various preference mechanisms remains an open research question. Previous research is in agreement that the optimal incentive in any type of preference system requires some a priori knowledge on the part of the buyer regarding the degree of disadvantage between the two types of sellers. If the preference is set too high, the representation of weaker sellers may increase but at an increased expense in procurement cost to the buyer. If the preference is set too low, the reasons for implementing the preference in the first place may not be accomplished. In the literature and in practice, three types of preference mechanisms have been investigated and used. Using a firstprice-sealed-bid (FPSB) auction format, Hellerstein et al., (2011) study the impact of a quota system where a number of items are set-aside for weaker sellers. Using an equilibrium approximation approach based on minimizing the gain a seller would realize from a unilateral change in bidding strategy, the authors estimate the equilibrium solutions for an auction having two types of sellers where quotas are set aside for the weaker type of sellers. A series of laboratory experiments are then run to see if the equilibrium approximations hold up in a laboratory setting. Experimental results show that savings from an imposed quota were greater in the laboratory than predicted by their equilibrium approximation. It is suggested that the quota system is a simple and effective way to discriminate between sellers as it decreases the available demand for the stronger sellers thereby resulting in such sellers adopting more aggressive bidding strategies. Another type of preference is that found in the Buy-American Act (Manuel, 2016). If a domestic seller, generally thought of as having higher production costs than a foreign seller, submits a bid that is less than some percent greater than that submitted by a foreign seller, the bid is awarded to the domestic seller. The percentages are 6 percent if the domestic seller is a large business, 12 percent if the domestic business is a small business, and 50 percent if the seller is a Department of Defense contractor. In this situation, the preference is used for comparative bid purposes only to decide who wins the auction as the winning bidder of each auction is paid their submitted bid amount. This is termed a price-preference auction in the sense that the winner of the auction may not be the seller who submits the lowest bid amount. Using a numerical approximation approach, Corns and Schotter (1999), estimate the equilibrium solution. In a series of laboratory experiments, bidding strategies and procurement costs are then compared to their equilibrium estimations. Results show that if the bidding preference is set correctly, the aggressive bidding by stronger sellers results in reduced bids that more than offset any increases paid to the weaker sellers. This paper studies the third type of preference, where a subsidy is offered to the weaker seller in the form of additional payments. In the FCC auctions discussed earlier, favored bidders who won the auction were offered a 40% discount on their winning bid and any bid won by a favored

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bidder was financed by the FCC at very favorable rates they would have been unlikely to get in the open market (Ayers and Cramton, 1996). The FCC auctions were a traditional auction in the sense that the several buyers were seeking to buy from one seller whereas in procurement or reverse auction, several sellers seek to sell to one buyer. The discount offered by the FCC and the reduction in financing costs can be viewed as a form of subsidy offered by the seller. In the case of a procurement auction, the preference is more obvious in that the seller is paid a subsidy over and above their submitted bid amount. If a weaker seller submits the lowest bid, he wins the auction and is paid his bid amount plus the subsidy (Rothkopf et al., 2003). As in the quota and the pricepreference auction discussed above, the proper subsidy requires that the buyer have prior knowledge about the relative disadvantage in cost between the strong and weak sellers. Whereas the first and second types of incentives have been studied experimentally (Hellerstein, et al., 2011 and Corns and Schotter, 1999), the subsidy preference has not. In the analytical paper by Rothkopf et al., (2003), a closed form model where weaker bidders are offered a subsidy in the form of additional payment is presented. Using a multiplicative bidding model, where sellers are restricted to bidding multiples of their estimated costs, equilibrium bidding strategies for a variety of model parameters is presented. Most of the previous studies on preference auctions assume that the only bidder uncertainty is restricted to the value of the item to his competitors. Recognizing that sellers are seldom certain about their costs (Milgrom 1981, Elmagrhraby 2007), Rothkopf et al. (2003) considers the case where bidders are uncertain as to the value of the item to themselves. Indeed, the assumption that sellers know their costs with certainty, the well-known Independent Private Value model, is likely untenable. Therefore, each type of seller receives an estimate of the actual cost rather than the actual cost itself. In this model, the uncertainty of cost for each seller, the cost estimation error, is drawn from identical Weibull distributions. In other words, all sellers face equal uncertainty regarding their ability to estimate their own costs. In this paper, we test the equilibrium predictions of the Rothkopf et al. (2003) model using a set of controlled experiments. Specifically, we investigate whether predictions regarding the equilibrium bidding strategies, expected profits, and buyer procurement costs can be duplicated in a behavioral experimental setting. In addition, we wish to determine the sensitivity of sellers to various subsidy settings other than the optimal suggested by the model since, for an optimal subsidy, the buyer requires prior knowledge of the relative cost disadvantage. In practice, such knowledge may not be known with certainty. Rothkopf et al. (2003) note that their results are somewhat insensitive to the requirement of prior knowledge of the relative cost differences, suggesting that a rather cautious subsidy set by the buyer is better than no subsidy at all. In other words, a partial subsidy that reduces the level of disadvantage is preferable to a full subsidy, and a full subsidy is preferable to no subsidy. Furthermore, we wish to determine how sensitive any results are to various levels of cost disadvantage. Results from Rothkopf et al. (2003)

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suggest that when an optimal subsidy is used, markups and expected profits for the two types of sellers are somewhat muted with respect to cost disadvantage. As the disadvantage increases, the stronger seller bids more aggressively and realizes a slight increase in profit while the weaker seller does the opposite.

(1) Do the bidding strategies of sellers in an experimental setting approximate those suggested by Rothkopf et al. (2003). In particular, will stronger sellers bid more aggressively when a subsidy is offered to weaker sellers compared to when no subsidy is offered? (2) How does the level of cost disadvantage affect the bidding strategies of the stronger and weaker sellers? Rothkopf et al. (2003) suggest that in the presence of subsidies, as the relative cost disadvantage increases, the weaker seller bids more aggressively thus realizes less profits. The stronger seller bids less aggressively and realizes an increase in profit. Any differences in bidding strategies and profits due to cost disadvantage are somewhat dampened if an optimal subsidy is used. (3) What is the impact on buyer procurement costs as the level of subsidy and cost disadvantage changes and How sensitive are sellers bidding strategies in a laboratory setting to the level of subsidy offered by the buyer? In addition to the political benefits realized by subsidizing less efficient bidders, another benefit is that buyer costs may actually decrease. Rothkopf et al. (2003)’s model suggests that it is not necessary to know the precise relationship between the costs of the stronger and weaker seller suggesting that a cautiously set subsidy will capture most of the positive benefits compared to no subsidy at all. We test whether Rothkopf et al. (2003)'s expected procurement cost have a similar pattern with the actual procurement cost.

2. SOME THEORY The Rothkopf et al. (2003) model with subsidies uses a multiplicative strategy model that limits bidders to bidding multiples of their cost estimate rather than some arbitrary function of the estimates. Let hi (ci′ ) = Pi (ci′ ) where hi (ci′ ) is the bid submitted by seller i given a cost estimate of ci′ and Pi is the markup multiplier. Consider an auction where a strong seller competes with a weak seller. Let ci be the cost for an item for seller i, (i = 1, 2, …, n). Assume each seller is not certain of their true costs to provide the item and instead prepares an estimate of this cost, c j′ = ρ c j where ρ be drawn from a two parameter Weibull distribution with a common shape parameter, m > 0, and scale parameter, a > 0. In their model, the degree of cost estimate uncertainty, u, is identical for all sellers and where u is the standard deviation of ρ j : (1) u = [Γ(1 + 2 / m) − Γ 2 (1 + 1 / m)]−1/ 2 Let c1 represent the cost for the stronger seller, c2 represent the cost for the weaker seller where c1 < c2 , and the cost

3. EXPERIMENTAL DESIGN

disadvantage between the two sellers, d, is the ratio of c2 c1 . The equilibrium bidding strategies for the two sellers is: (2) P1 = mX (d )[1 + X (d )]1/ m [mX (d ) − 1],

P2 = m[1 + 1/ X (d )]1/ m [m − X (d )],

(3)

where

X (d )= {m(1 − d ) + [m 2 (1 − d ) 2 + 4d ]1/ 2 } 2, and X (d ) is a function of the shape parameter m.

(4)

Building on the multiplicative model presented by Rothkopf et al. (1969), Rothkopf et al. (2003) consider a discriminatory auction where the buyer offers to incentivize the weaker seller by paying him his bid amount plus a subsidy, s, over and above his submitted bid. In this situation, a rational bidder will bid as if seller 2’s cost is actually= c2 s c2 (1 + s ) where the disadvantage ratio is d c2 [c1 (1 + s )] . Since the = probability that seller 2 wins is defined by: X (d ) [1 + X (d )] , the expected amount paid due to the subsidy is: (c2 − c2 s ) X (d ) [1 + X (d )] . This results in an expected procurement cost of = Z md [m − X (d )] + (c2 − c2 s ) X (d ) [1 + X (d )] . For various levels of cost uncertainty and cost disadvantage, the authors present optimal subsidy amounts, bidding strategies and resulting profits for each type of seller as well as the expected procurement cost to the buyer. In this analytical model, several predictions are made. It is these predictions that we empirically investigate in a series of controlled experiments. Specifically:

The experiments conducted are represented a discriminatory auction where a weaker seller is offered an incentive in the form of a subsidy. Participants were recruited from an introductory Supply Chain Management course normally taken during the third year of their study at a major US State University. Upon arrival, each student was given a set of instructions based on whether they were a weak seller or a strong seller. Additional information was then read out loud by one of the experimental administrators and any questions were answered. Each of the participants was acting in the role of a construction company competing for the rights to build a bridge for the state Department of Transportation (DOT) in a series of 25 sealed-bid first-price auctions. For each auction, the cost to complete a hypothetical project for an advantaged seller, c1 , is drawn from a uniform distribution, U (100, 000 − 400, 000) . Based on actual bid data from the DOT, this range of project costs represents nearly 40 percent of all projects posted for bidding. Rothkopf et al. (2003) suggests that the size of the project should not influence seller bidding strategies. Based on the level of cost disadvantage, the cost of the project for the weaker seller, c2 , is calculated by multiplying the cost for the stronger seller, c1 , by the disadvantage: c2= c1 × d . Each seller is aware of the level of (dis)advantage and the distribution from where project costs are drawn. However, rather than knowing the exact project cost, each seller is given an estimate of the cost. As in Rothkopf et al. (2003), the uncertainty of project costs is introduced by multiplying the true but unknown project costs for each seller, c1 and c2 by a random variable, ρi , common

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to both sellers. Recall that ρi is drawn from a two parameter Weibull distribution with a common shape parameter, m > 0, and scale parameter, a > 0. Consider, if it is fairly common knowledge that a weaker seller has a five percent cost disadvantage relative to a stronger seller, his cost estimate will be drawn from a distribution that is five percent higher at every level of probability. In other words, the uncertainty regarding project cost is identical between sellers. For each auction, students prepared and submitted bid amounts, the winner/loser of each auction was revealed to each seller. The profits from each auction were revealed to the winning seller. 3.1 Treatments and Protocol To investigate our research questions, we vary two key aspects: the cost disadvantage and the level of subsidy offered to the weaker seller. First, we choose two levels of cost disadvantage, d = 1.05 and d = 1.20, for which equilibrium results are presented in Rothkopf et al. (2003). Second, we choose four different levels of subsidies for each level of cost disadvantage: a full subsidy, the optimal subsidy, one-half of the optimal subsidy, and no subsidy. Given two levels of cost advantage and four levels of subsidy results in eight scenarios studied in the lab. Column 1 in Table 1 presents the design of our experiments as well as the number of participants in each scenario. We use the z-Tree software platform (Fischbacher 2007) to conduct all auctions. An even number of participants were used for all treatments who were randomly assigned to one of two type sellers. All participants remained in the same type for the entire session. For each of the 25 auctions, participants from each type were randomly paired. The first five auctions from each session were used to familiarize participants with the experiment. Results were collected for the remaining 20 auctions. For the main experiment, 170 undergraduate students participated in total. Each student was paid a tendollar incentive for showing up and had the opportunity to earn additional funds based on their performance during the study. In addition, an added incentive was offered in the form of credit for one homework grade for all students who participated. The majority of experimental papers use student participants rather than industry practitioners due to convenience and accessibility. However, research has shown that there is no discernible difference in the behaviour of both groups (Donohue at al., 2019) in studies such as ours. Students can think cognitively and, if properly incentivized, can behave in a rational manner. 4. ANALYSIS AND RESULTS Table 1 presents our experimental results for two levels of cost advantage, 1.05 and 1.2, and four levels of preference/subsidy, full subsidy, optimal subsidy, partial subsidy and no subsidy. Column 2 shows the settings of our two factors of interest that results in the eight treatments. The theoretical predictions using the Rothkopf et al. (2003) model are also provided as well as the deviations from the experimental and theoretical calculations. Columns 3 – 4 present the results for the weaker sellers while columns 5 – 6 show the results for the stronger sellers. Column 7 shows the expected procurement costs for each treatment.

1993

Research Question 1. Are bidder strategies consistent with theoretical predictions? The bidding strategies of both types of sellers is much more aggressive than that predicted by theory (comparing columns 4a to 4b and 6a to 6b) to the extent that the weaker seller often realizes a negative profit while the stronger seller realizes a profit that is significantly less than predicted (comparing columns 3a with 3b and 5a with 5b). Additionally, results show that the weaker sellers in most cases submits much more aggressive bids than the stronger seller as the level of subsidy is increased. This is contrary to that predicted by theory. The strong seller does bid more aggressively as predicted but at a much lower markup. In general, theory predicts that the stronger seller will submit more aggressive bids as the level of subsidy increases in response to the increased competition represented by subsidizing the weaker sellers. We do not find that to be true. Research Question 2. What is the impact of the level of cost disadvantage on the bidding strategies of the disadvantaged and advantaged sellers? Rothkopf et al. (2003) suggests that the stronger seller will submit less aggressive bids as the cost difference increases while the difference in cost has a minimal effect on the bidding behavior of the disadvantaged bidder. In our results, we find that the pattern of behavior by the weaker seller is consistent with predictions although at a much less aggressive level. The behavior of the stronger seller is somewhat mixed based on the treatment settings. The strong seller’s strategy changes only slightly as the cost difference increases while the strategy of the weaker seller changes dramatically, even to the point of negative markups. It appears that the weaker seller uses the subsidy to try to make up for their cost disadvantage in case they win an auction. In summary, the weaker seller submits much more aggressive bids in the presence of subsidies as the cost difference increases than is theoretically predicted. Research Question 3. What is the impact on buyer procurement costs as the level of subsidy and cost disadvantage change (column 7a and column 7b)? Due to the more aggressive bidding by both types of bidders, regardless of cost disadvantage or subsidy level, actual procurement costs are much less than predicted by theory. The effects of subsidy on procurement costs are mixed while the impact of cost disadvantage is more straightforward. As the cost disadvantaged increases, the cost to the buyer increases despite the subsidy used. 5. CONCLUSION This paper tests the predictions of the Rothkopf et al (2003) model. The levels of subsidy are vital to both buyers and policymakers such that if buyers fail to assign the correct levels of subsidies it would hurt not only the welfare of weaker sellers but also the profit of buyers. Rothkopf et al. (2003) provides the equilibrium results to help policymakers and buyers choose the most advantageous subsidy level given levels of cost disadvantage. We find that the behavior of both types of bidders is much different from that predicted by the model. In order for such auctions to be effective, it is important to understand not just theoretical predictions, but also the behavioral tendencies of bidders. The fact that

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Table 1. Treatments and observed experimental results with theoretical results 1

2

3a

3b

3c

4a

4b

4c

5a

5b

Firm A (Weak Firm)

5c

6a

6b

6c

7a

7b

7c

Firm B (Strong Firm)

# of Deviation Deviation Deviation Deviation Actual Predicted Deviation Cost Sub Avg. Predicted Avg. Predicted Avg. Predicted Avg. Predicted TrtAucfrom from from from ProcurementProcurement from Ratiosidy Profit Profit Markup Markup Profit Profit Markup Markup tion Theory Theory Theory Theory Cost Cost Theory 1 240 1.05 0 -2.04

4.10

6.14

9.59

17.90

8.31

2.00

7.90

5.90

8.56

21.10

12.54

1.82

14.20

12.38

2 180 1.05 36 1.52

3.60

2.08

6.52

17.90

11.38

1.73

7.20

5.47

16.49

21.10

7.2

6.08

13.00

6.92

3 200 1.05 72* 0.89

5.10

4.21

8.40

18.70

10.30

3.09

6.10

3.01

14.38

19.60

5.22

6.22

13.80

7.58

4 220 1.05 100 -0.29

5.60

5.89

3.51

19.10

15.59

-1.26

5.60

6.86

7.07

19.10

12.03

0.85

13.50

12.65

5 220# 1.20 0 -1.85

2.00

3.85

6.54

17.50

10.96

8.53

17.60

9.07

19.73

31.20

11.47

14.5

26.10

11.6

6 200# 1.20 35.5 -3.84

2.80

6.64

-2.64

17.40

20.04

4.22

12.00

7.78

13.19

25.30

12.11

8.96

23.00

14.04

7 200 1.20 71* -0.30

4.10

4.40

-3.30

17.90

21.20

2.79

7.90

5.11

14.55

21.20

6.65

10.64

21.50

10.86

8 180# 1.20 100 1.01

5.60

4.59

-4.21

19.10

25.39

0.62

5.60

4.98

14.05

19.10

5.05

11.22

22.22

11.00

Note: # denotes that one student in each treatment did not meaningfully participate as they fail to understand the experiment. We removed all of their participated auctions. * represents the optimal subsidy estimated by Rothkopf et al. (2003). CV is set to 0.12 for all scenarios. All values are percentages.

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bidders in an auction do not bid according to equilibrium predictions is well known. Such behaviors have been attributed to “joy of winning”, “risk aversion”, “spiteful bidding”, “regret”, “overconfidence” to name a few. To discover the exact reasons why bidders overbid (underbid in a procurement auction) is an ongoing research area that warrants future study. REFERENCES Ayers, I., and Cramton P. (1996). Deficit Reduction Through Diversity: How Affirmative Action at the FCC Increased Auction Competition. Stanford Law Review, 48, 761-815. Corns, A., and Schotter, A. (1999). Can affirmative action be cost effective? An experimental examination of pricepreference auctions. American Economic Review, 89(1), 291-305. Donohue, K., E. Katok, and S. Leider (2019). The Handbook of Behavioral Operations. John Wiley & Sons, Hoboken, NJ. Fischbacher, U. (2007). z-Tree: Zurich toolbox for readymade economic experiments. Experimental Economics, 10(2), 171-178. Hellersteina, D., Higginsa, N., and Robertsb, M. J. (2011). Using quotas to enhance competition in asymmetric auctions: A comparison of theoretical and experimental outcomes. Games and Economic Behavior. Manuel, K. M. (2016). The Buy American Act—Preferences for “Domestic” Supplies: In Brief. Congressional Research Service. McAfee, R. P., and McMillan, J. (1989). Government procurement and international trade. Journal of International Economics, 26(3-4), 291-308. Myerson, R. B. (1981). Optimal auction design. Mathematics of Operations Research, 6(1), 58-73. Rothkopf, M. H. (1969). A model of rational competitive bidding. Management Science, 15(7), 362-373. Rothkopf, M. H., Harstad, R. M., and Fu, Y. (2003). Is subsidizing inefficient bidders actually costly?. Management Science, 49(1), 71-84.

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