Academic journal article Journal of Economics and Economic Education Research

A Systematic Presentation of Equilibrium Bidding Strategies to Undergraduate Students

Academic journal article Journal of Economics and Economic Education Research

A Systematic Presentation of Equilibrium Bidding Strategies to Undergraduate Students

Article excerpt

INTRODUCTION

Auctions have always been a large part of the economic landscape, with some auctions reported as early as in Babylon in about 500 B.C. and during the Roman Empire, in 193 A.D. (3) Auctions with precise set of rules emerged in 1595, where the Oxford English Dictionary first included the entry; and auctions houses like Sotheby's and Christie's were founded as early as 1744 and 1766, respectively. Commonly used auctions nowadays, however, are often online, with popular websites such as eBay, with US$11 billion in total revenue and more than 27,000 employees worldwide, which attracted the entry of several competitors into the online auction industry, such as QuiBids recently.

Auctions have also been used by governments throughout history. In addition to auctioning off treasury bonds, in the last decade governments started to sell air waves (3G technology). For instance, the British 3G telecom licenses generated Euro 36 billion in what British economists called "the biggest auction ever," and where several game theorists played an important role in designing and testing the auction format before its final implementation. In fact, the specific design of 3G auctions created a great controversy in most European countries during the 1990s since, as the following figure from McKinsey (2002) shows, countries with similar population collected enormously different revenues from the sale, thus suggesting that some countries (such as Germany and the UK) better understood bidders' strategic incentives when participating in these auctions, while others essentially overlooked these issues, e.g., Netherlands or Italy.

Despite the rapidly expanding literature using auction theory, only a few graduate-level textbooks about this topic have been published; such as Krishna (2002), Milgrom (2004), Menezes and Monteiro (2004) and Klemperer (2004). These textbooks, however, introduce auction theory to upper-level (second year) Ph.D. students, using advanced mathematical statistics and, hence, are not accessible for undergraduate students. In addition, most undergraduate textbooks do not cover the topic, or present short verbal descriptions about it; see, for instance, Pindyck and Rubinfeld (2012) pp. 516-23, Perloff (2011) pp. 462-66, or Besanko and Braeutigam (2011) pp. 633-42. (4) In order to provide an attractive introduction to auction theory to undergraduate students, this paper only assumes a basic knowledge of algebra and calculus, and uses worked-out examples and figures. As a consequence, the explanations are appropriate for intermediate microeconomics and game theory courses, both for economics and business majors. In particular, the paper emphasizes the common ingredients in most auction formats (understanding them as allocation mechanism). Then, it analyzes optimal bidding behavior in first-price auctions (section three) and in second-price auctions (section four). Finally, section five examines bidding strategies in common-value auctions and the winner's curse.

AUCTIONS AS ALLOCATION MECHANISMS

Consider Nbidders who seek to acquire a certain object, where each bidder i has a valuation [v.sub.i] for the object, and assume that there is one seller. Note that we can design many different rules for the auction, following the same auction formats we commonly observe in real life settings. For instance, we could use:

1. First-price auction (FPA), whereby the winner is the bidder submitting the highest bid, and he/she must pay the highest bid (which in this case is his/hers).

2. Second-price auction (SPA), where the winner is the bidder submitting the highest bid, but in this case he/she must pay the second highest bid.

3. Third-price auction, where the winner is still the bidder submitting the highest bid, but now he/she must pay the third highest bid.

4. All-pay auction, where the winner is still the bidder submitting the highest bid, but in this case every single bidder must pay the price he/she submitted. …

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