Field experiments on the effects of reserve prices in auctions: more Magic on the Internet.

I present experimental evidence on the effects of minimum bids in first-price, sealed-bid auctions. The auction experiments manipulated the minimum bids in a preexisting market on the Internet for collectible trading cards from the game Magic: the Gathering. I examine a number of outcomes, including the number of participating bidders, the probability of sale, the levels of individual bids, and the auctioneer's revenues. The benchmark theoretical model is one with symmetric, risk-neutral bidders with independent private values. The results verify a number of the predictions concerning equilibrium bidding. Many bidders behave strategically, anticipating the effects of the reserve price on others' bids.

1. Introduction

There has been considerable theoretical work on the effects of minimum bids (or reserve prices) in auctions, but little empirical work. This article represents an attempt to fill this gap. I report experimental tests of the theory of reserve prices in first-price, sealed-bid auctions, using field experiments in a preexisting market. The experimental data verify the predictions of the theoretical model developed by Vickrey (1961) and extended by Riley and Samuelson (1981). In particular, bidders exhibit sophisticated strategic reactions to changes in reserve prices, as predicted by the theory. In addition, I present empirical results on the relationship between mean revenues and the minimum-bid level.

Empirical studies of auctions can be divided into laboratory experiments and field-data studies. Dozens of laboratory experiments have tested different predictions of auction theory (Kagel, 1995). Empirical work using field data is more limited in testing theory because of data restrictions (Hendricks and Paarsch, 1995). My methodology is a hybrid of the laboratory and traditional field research, hence the term "field experiment." In Lucking-Reiley (1999), I used a similar methodology to test revenue equivalence of auction formats.

Neither laboratory nor field studies have focused much attention on the levels of reserve prices. (1) A few studies of eBay auctions, such Bajari and Hortaqsu (2003), include the effects of minimum-bid levels in their regression results, but this is not the main focus of their work. By systematically varying reserve-price levels, I confirm several predictions of auction theory: increasing the reserve price decreases the number of bids received and the probability of selling the good, and increases revenue for goods that are actually sold. Perhaps most interesting is the result that bidders react strategically to the existence of reserve prices, as predicted by Bayesian Nash equilibrium theory.

The article is organized as follows. In Section 2, I review the testable implications of the effects of reserve prices in auctions, based mainly on Riley and Samuelson (1981). Section 3 describes the history and institutional details of the marketplace for collectible trading cards, where these field experiments took place. In Section 4, I describe the two experimental designs used in this study, along with a demographic description of the experimental subjects. Section 5 describes the results of the experiments, and the article concludes with a brief summary and suggestions for future research.

2. Theoretical background