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This textbook provides a short introduction to auction theory through exercises with detailed answer keys. Focusing on practical examples, this textbook offers over 80 exercises that predict bidders’ equilibrium behaviour in different auction formats, along with the seller’s strategic incentives to organize one auction format over the other. The book emphasizes game-theoretic tools, so students can apply similar tools to other auction formats. Also included are several exercises based on published articles, with the model reduced to its main elements and the question divided into several easy-to-answer parts. Little mathematical background in algebra and calculus is assumed, and most algebraic steps and simplifications are provided, making the text ideal for upper undergraduate and graduate students.

The book begins with a discussion of second-price auctions, which can be studied without using calculus, and works through progressively more complicated auction scenarios: first-price auctions, all-pay auctions, third-price auctions, the Revenue Equivalence principle, common-value auctions, multi-unit auctions, and procurement auctions. Exercises in each chapter are ranked according to their difficulty, with a letter (A-C) next to the exercise title, which allows students to pace their studies accordingly. The authors also offer a list of suggested exercises for each chapter, for instructors teaching at varying levels: undergraduate, Masters, Ph.D.

Providing a practical, customizable approach to auction theory, this textbook is appropriate for students of economics, finance, and business administration. This book may also be used for related classes such as game theory, market design, economics of information, contract theory, or topics in microeconomics.

### 1. Second-Price Auctions

Abstract
We start our analysis of auction formats with the second-price auction, where the winning bidder does not pay the bid he submitted but, instead, the second-highest bid. This auction format is relatively easy to analyze, requiring limited mathematical steps, and thus we believe that it can serve as a first approximation to bidding behavior for non-technical readers. Examples of this auction format include eBay sales, auctioning radio spectrums, and the pricing that search engines, such as Google, Bing, or Yahoo, use to sell keyword-based advertising.
Pak-Sing Choi, Felix Munoz-Garcia

### 2. First-Price Auctions

Abstract
In this chapter, we analyze first-price auctions, where every bidder privately observes his valuation for the object and submits his bid to the seller (e.g., in a sealed envelope). The seller ranks all bids, selects as a winner the bidder who submitted the highest bid to pay the bid he submitted. All other bidders pay zero and not receive the object.
Pak-Sing Choi, Felix Munoz-Garcia

### 3. First-Price Auctions: Extensions

Abstract
This chapter applies the analysis of equilibrium bidding behavior in first-price auctions from Chap. 2 to answer different questions. In Exercise 3.1, we measure the seller’s expected revenue in this auction format when bidders draw their valuations from a generic distribution function and then evaluate this expected revenue in the case that bidders’ valuations are uniformly distributed.
Pak-Sing Choi, Felix Munoz-Garcia

### 4. All-Pay Auctions and Auctions with Asymmetrically Informed Bidders

Abstract
In this chapter, we study all-pay auctions. As in the auction formats we examined in previous chapters, every bidder submits his bid and the bidder submitting the highest bid wins the object. However, as opposed to other auctions where only the winning bidder must pay for the object (either the highest or second-highest bid), in the all-pay auction every bidder must pay the bid that he submitted. As expected, this makes bidders less aggressive in their bids than in other auction formats, which we demonstrate to hold under different settings. Examples of all-pay auctions include contests, political campaigns, awarding of monopoly licenses, and R&D races where players (e.g., firms) cannot recover their participation costs upon losing. More recently, we can also find this type of auctions being used by internet sellers such as QuiBids.​com, which requires bidders to purchase tokens/points before an auction starts, and then submit their token bids, which cannot be recovered regardless of the outcome of the auction.
Pak-Sing Choi, Felix Munoz-Garcia

### 5. Third-Price Auctions, kth-Price Auctions, and Lotteries

Abstract
This chapter generalizes previous auction formats by allowing the winning bidder to pay the kth highest bid, while all losing bidders pay zero. This implies that in the first-price auction, we have that k = 1, as the winning bidder pays the highest bid; and in the second-price auction, k = 2, as he pays the second-highest bid. A similar argument applies to the third-price auction, where k = 3, as the winning bidder pays the third-highest bid, and, more generally, to any other auction format where k > 3.
Pak-Sing Choi, Felix Munoz-Garcia

### 6. The Revenue Equivalence Principle

Abstract
In this chapter, we evaluate the seller’s expected revenue in different auction formats and show under which contexts this revenue is equivalent. First, Exercise 6.1 considers the first-price, second-price, third-price, and all-pay auctions from the previous chapters, evaluating the expected revenue that each of them generate, and showing that the expected revenue coincides.
Pak-Sing Choi, Felix Munoz-Garcia

### 7. Common-Value Auctions

Abstract
This chapter examines auctions where all bidders share the same (common) value for the object, but none of them observe an accurate signal of the object’s true valuation. Instead, every bidder privately observes a noisy signal about the object’s value and, based on this signal, submits a bid. This model is typically used to analyze the auctioning of oil leases, as firms exploiting the oil reservoir would earn a similar profit if they win the auction, but they have imprecise and potentially different signals of the amount of oil barrels in the reservoir (as they receive different engineering reports) and, as a consequence, hold different estimates of the oil lease’s profitability.
Pak-Sing Choi, Felix Munoz-Garcia

### 8. Multi-Unit Auctions

Abstract
In this chapter we introduce the reader to auctions where the seller offers more than one unit (multi-unit auctions).
Pak-Sing Choi, Felix Munoz-Garcia

### 9. Mechanism Design

Abstract
Previous chapters consider different auction formats, understood as mechanisms to allocate an object among different individuals (bidders). Each of them is, essentially, characterized by an allocation rule (who gets the object) and a payment rule (how much each bidder has to pay when winning the object and otherwise). In this chapter, we take a more general approach by considering a richer set of mechanisms, seeking to: (1) allocate the object to the individual with the highest valuation (efficiency); (2) maximize the seller’s expected revenue; (3) maximize the social planner’s welfare function; or (4) a combination of these objectives.
Pak-Sing Choi, Felix Munoz-Garcia

### 10. Procurement Auctions

Abstract
This chapter examines procurement auctions, such as those that utility companies use to deliver water or garbage collection services, under different settings. In these auctions, firms compete to be awarded the service delivery contract, privately observe their costs, and bid to a social planner who seeks to award the contract to the most efficient firm (lowest cost).
Pak-Sing Choi, Felix Munoz-Garcia