Publications
Position Auctions with Multi-unit Demands [PDF]
Games and Economic Behavior, Volume 127, May 2021
presented at: Conference on Economic Design, Budapest, Hungary, June 2019
This paper studies the design of position auctions when bidders have multi-unit demands for advertising slots. I propose an ascending clock auction with two stages: allocation stage and assignment stage. The allocation stage determines the quantity of positions assigned to each advertiser using a generalized version of the Ausubel (2004) Auction under the context of differentiated items. The assignment stage determines the ranking of advertisements using a generalized version of the Generalized English Auction under the context of multi-unit demands. I show that this two-stage ascending clock auction can implement the VCG outcome in an ex-post perfect equilibrium under pure private values.
Auctions with Quantity Externalities and Endogenous Supply [PDF]
International Journal of Industrial Organization, Volume 71, July 2020
presented at: Midwest Theory Conference, Indiana University Bloomington, May 2019
This paper studies the design of license auctions when the number of licenses allocated in the auction determines structure of the downstream market. I first show that a sequence of conditional reserve prices that specify minimum acceptable bid at each supply level can be used to determine supply endogenously. Then I construct a static auction called multi-dimensional uniform-price auction that allows the auctioneer to condition reserve price on supply and allows bidders to condition bids on supply. I also construct a dynamic auction called Walrasian clock auction that adjusts supply through a tatonnement process. I show that both proposed auctions can implement the efficient market structure in a dominant strategy equilibrium. I next characterize the optimal auction and show that the two proposed auctions can yield the optimal revenue under a sequence of optimal reserve prices.
Working Papers
Position Auctions with Interdependent Values, 2017 [PDF] [Slides]
presented at:
Midwest Theory Conference, Southern Methodist University, November 2017;
12th Economic Graduate Student Conference, Washington University in St. Louis, October 2017;
Young Economist Symposium, Yale University, August 2017
This paper extends the theoretical study of position auctions to an interdependent values model in which each bidder’s value depends on its opponents’ information as well as its own information. Position auctions are used by major search engines to allocate multiple advertising links on search result pages. In this paper, I examine efficiency and revenues of three position auction formats: Generalized Second Price (GSP) auctions, VCG-like auctions, and Generalized English Auctions (GEA). I find that both the GSP auction and the VCG-like auction with one-dimensional bidding language can be inefficient under interdependent values, which contrasts previous literature that favors the GSP auction for its simplicity. I next show this inefficiency problem can be fully resolved by adopting a multi-dimensional bidding language that allows bidders to bid differently across positions. Moreover, the dynamic GEA that implicitly adopts a multi-dimensional bidding language always implements efficiency in an ex-post equilibrium. Then I provide a revenue ranking of the three efficient position auctions and characterize the optimal position auction subject to no reserve price under interdependent values. I find that under independent signals and a set of regularity conditions, the three efficient position auctions also implement the optimal revenue subject to no reserve price.
Information Provision in Procurement Auctions with Endogenous Investments, 2016 [PDF]
This paper analyzes an auctioneer's optimal information provision strategy in a procurement auction in which horizontally differentiated suppliers engage in cost-reducing investments before entering the auction. In this paper, I characterize the bidders’ equilibrium investment strategies under three different information provision schemes: public disclosure, private disclosure, and concealment of preferences over bidders’ product characteristics. I find that pre-auction investments are strategic substitutes among bidders. Providing more information about the auctioneer's preference encourages those favored bidders to invest more, which results in a more dispersed distribution of costs in the auction. Then I compare the expected revenues in a second-score auction under these three information provision schemes. I show that concealment is optimal with two bidders, while public disclosure is optimal with a sufficiently large number of bidders.
Position Auctions with Multi-unit Demands [PDF]
Games and Economic Behavior, Volume 127, May 2021
presented at: Conference on Economic Design, Budapest, Hungary, June 2019
This paper studies the design of position auctions when bidders have multi-unit demands for advertising slots. I propose an ascending clock auction with two stages: allocation stage and assignment stage. The allocation stage determines the quantity of positions assigned to each advertiser using a generalized version of the Ausubel (2004) Auction under the context of differentiated items. The assignment stage determines the ranking of advertisements using a generalized version of the Generalized English Auction under the context of multi-unit demands. I show that this two-stage ascending clock auction can implement the VCG outcome in an ex-post perfect equilibrium under pure private values.
Auctions with Quantity Externalities and Endogenous Supply [PDF]
International Journal of Industrial Organization, Volume 71, July 2020
presented at: Midwest Theory Conference, Indiana University Bloomington, May 2019
This paper studies the design of license auctions when the number of licenses allocated in the auction determines structure of the downstream market. I first show that a sequence of conditional reserve prices that specify minimum acceptable bid at each supply level can be used to determine supply endogenously. Then I construct a static auction called multi-dimensional uniform-price auction that allows the auctioneer to condition reserve price on supply and allows bidders to condition bids on supply. I also construct a dynamic auction called Walrasian clock auction that adjusts supply through a tatonnement process. I show that both proposed auctions can implement the efficient market structure in a dominant strategy equilibrium. I next characterize the optimal auction and show that the two proposed auctions can yield the optimal revenue under a sequence of optimal reserve prices.
Working Papers
Position Auctions with Interdependent Values, 2017 [PDF] [Slides]
presented at:
Midwest Theory Conference, Southern Methodist University, November 2017;
12th Economic Graduate Student Conference, Washington University in St. Louis, October 2017;
Young Economist Symposium, Yale University, August 2017
This paper extends the theoretical study of position auctions to an interdependent values model in which each bidder’s value depends on its opponents’ information as well as its own information. Position auctions are used by major search engines to allocate multiple advertising links on search result pages. In this paper, I examine efficiency and revenues of three position auction formats: Generalized Second Price (GSP) auctions, VCG-like auctions, and Generalized English Auctions (GEA). I find that both the GSP auction and the VCG-like auction with one-dimensional bidding language can be inefficient under interdependent values, which contrasts previous literature that favors the GSP auction for its simplicity. I next show this inefficiency problem can be fully resolved by adopting a multi-dimensional bidding language that allows bidders to bid differently across positions. Moreover, the dynamic GEA that implicitly adopts a multi-dimensional bidding language always implements efficiency in an ex-post equilibrium. Then I provide a revenue ranking of the three efficient position auctions and characterize the optimal position auction subject to no reserve price under interdependent values. I find that under independent signals and a set of regularity conditions, the three efficient position auctions also implement the optimal revenue subject to no reserve price.
Information Provision in Procurement Auctions with Endogenous Investments, 2016 [PDF]
This paper analyzes an auctioneer's optimal information provision strategy in a procurement auction in which horizontally differentiated suppliers engage in cost-reducing investments before entering the auction. In this paper, I characterize the bidders’ equilibrium investment strategies under three different information provision schemes: public disclosure, private disclosure, and concealment of preferences over bidders’ product characteristics. I find that pre-auction investments are strategic substitutes among bidders. Providing more information about the auctioneer's preference encourages those favored bidders to invest more, which results in a more dispersed distribution of costs in the auction. Then I compare the expected revenues in a second-score auction under these three information provision schemes. I show that concealment is optimal with two bidders, while public disclosure is optimal with a sufficiently large number of bidders.