## An Introduction to Auction Theory"The practical importance of auction theory is widely recognized. Indeed, economists have been recognized for their contribution to the design of several auction-like mechanisms, such as the U. S. Federal Communications Commission spectrum auctions, the 3G auctions in Europe and beyond, and the auction markets for electricity markets around the world. Moreover, auction theory is now seen as an important component of an economist's training. For example, some of the more celebrated results from the single-object auction theory are now usually taught in advanced undergraduate and first-year graduate courses on the economics of information. The techniques and insights gained from the study of auction theory provide a useful starting point for those who want to venture into the economics of information, mechanism design, and regulatory economics. This book provides a step-by-step, self-contained treatment of the theory of auctions. The aim is to provide an introductory textbook that will allow students and readers with a calculus background to work through all the basic results. Coverage includes: the basic independent-private-model; the effects of introducing correlation in valuations on equilibrium behaviour and the seller's expected revenue; mechanism design; and the theory of multi-object auctions. The paperback edition of the text includes a new chapter which acts as a guide to current developments in auction theory." -- BACK COVER. |

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### Contents

Introduction | 1 |

Private Values | 13 |

Common Value | 39 |

Affiliated Values | 57 |

Mechanism Design | 75 |

Multiple Objects | 121 |

A Probability | 145 |

B Differential Equations | 159 |

Index of Notations 173 | |

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### Common terms and phrases

affiliation allocation assume auction formats auction theory bidder 1 bids bidder l's button Chapter choose common value conditional consider continuous convex define Definition denote density differential equation distribution English equal equation equilibrium bidding strategy example exists expected payment expected profits expected utility first-price auction function given Hence highest highest bid implies incentive compatible independent individual integrating interval Lemma marginal maximizes maximum mean mechanism Note object obtain optimal auction participation pays player possible private values probability Proof prove random variable reader reason receives Remark reserve price result Revenue Equivalence Riemann integrable rule satisfies second highest second-price auction seller's expected revenue signal solve space strictly increasing Suppose surplus symmetric equilibrium Theorem true uniform valuation values model vector wins write yields zero