<p><strong><font size="3">Auction Theory <!--Element not supported - Type: 8 Name: #comment--><br/></font></strong>by <a href="http://www.amazon.com/exec/obidos/search-handle-url/002-5237687-7445669?%5Fencoding=UTF8&amp;search-type=ss&amp;index=books&amp;field-author=Vijay%20Krishna"><font color="#003399">Vijay Krishna</font></a> (Author)</p><p><a href="http://www.amazon.com/gp/reader/012426297X/ref=sib_dp_pt/002-5237687-7445669#reader-link"><img id="prodImage" height="240" alt="Auction Theory" src="http://ecx.images-amazon.com/images/I/41kLt56XpRL._BO2,204,203,200_PIsitb-dp-500-arrow,TopRight,45,-64_OU01_AA240_SH20_.jpg" width="240" border="0"/></a></p><li><b>Hardcover:</b> 316 pages </li><li><b>Publisher:</b> Academic Press; 1st edition (March 1, 2002) </li><li><b>Language:</b> English </li><li><strong>Review<br/></strong>"Vijay Krishna's book provides a very thorough and patient presentation of auction theory, starting from the most basic analysis and graduating to sophisticated, state of the art theory, including multi-unit auctions. This book covers a very wide range of auction topics, providing a clear and accessible treatment. The theory is presented in a careful and easily understood style accessible to honors undergraduates as well as all economics graduate students. Krishna's book will certainly become the central book on auction theory."<br/>--<strong><font color="#ff0000">R. Preston McAfee</font></strong>, Murray S. Johnson Chair in Economics, University of Texas<br/>"This book not only sets out much of the theoretical literature on auctions--including results that are very recent--but does so with a clarity, elegance, and rigor that is characteristic of Vijay Krishna's work."<br/>--<strong><font color="#ff0000">Eric Maskin</font></strong>, A.O. Hirschman Professor of Social Science, Institute for Advanced Study, Princeton, New Jersey, U.S.A.<br/>"The book gives a superb presentation of auction theory, with clear and concise proofs of all results. It is essential reading for any serious student of auctions."<br/>--<strong><font color="#ff0000">Peter Cramton</font></strong>, Professor of Economics, University of Maryland<br/>"This is the book we have been waiting for: a high level treatment of auction theory that carefully presents the technical details necessary for an in depth understanding of the main themes of auction theory, ideal as a basis for a graduate course, and by an author who has himself made important contributions to the subject."<br/>--<strong><font color="#ff0000">Paul Klemperer</font></strong>, Edgeworth Professor of Economics, Nuffield College, University of Oxford, U.K. <br/><br/>
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</li><li><strong><font size="4">Contents</font><br/>Preface ix<br/>1 Introduction 1</strong><br/>I Single Object Auctions 11<br/><strong>2 Private Value Auctions: A First Look 13</strong><br/>2.1 The SymmetricModel . . . . . . . . . . . . . . . . . . . . . 14<br/>2.2 Second-Price Auctions . . . . . . . . . . . . . . . . . . . . . 15<br/>2.3 First-Price Auctions . . . . . . . . . . . . . . . . . . . . . . 16<br/>2.4 Revenue Comparison . . . . . . . . . . . . . . . . . . . . . . 20<br/>2.5 Reserve Prices . . . . . . . . . . . . . . . . . . . . . . . . . 24<br/><strong>3 The Revenue Equivalence Principle 29</strong><br/>3.1 Main Result . . . . . . . . . . . . . . . . . . . . . . . . . . . 29<br/>3.2 Some Applications of the Revenue Equivalence Principle . . 31<br/>3.2.1 Unusual Auctions . . . . . . . . . . . . . . . . . . . . 31<br/>3.2.2 Uncertain Number of Bidders . . . . . . . . . . . . . 34<br/><strong>4 Qualifications and Extensions 37<br/></strong>4.1 Risk-Averse Bidders . . . . . . . . . . . . . . . . . . . . . . 38<br/>4.2 Budget Constraints . . . . . . . . . . . . . . . . . . . . . . . 42<br/>4.2.1 Second-Price Auctions . . . . . . . . . . . . . . . . . 43</li><p>4.2.2 First-Price Auctions . . . . . . . . . . . . . . . . . . 45<br/>4.2.3 Revenue Comparison . . . . . . . . . . . . . . . . . . 45<br/>4.3 Asymmetries among Bidders . . . . . . . . . . . . . . . . . 46<br/>4.3.1 Asymmetric First-Price Auctions with Two Bidders 46<br/>4.3.2 Revenue Comparison . . . . . . . . . . . . . . . . . . 51<br/>4.3.3 Efficiency Comparison . . . . . . . . . . . . . . . . . 54<br/>4.4 Resale and Efficiency . . . . . . . . . . . . . . . . . . . . . . 54<br/><strong>5 Mechanism Design 61</strong><br/>5.1 Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . 62<br/>5.1.1 The Revelation Principle . . . . . . . . . . . . . . . 62<br/>5.1.2 Incentive Compatibility . . . . . . . . . . . . . . . . 63<br/>5.1.3 Individual Rationality . . . . . . . . . . . . . . . . . 67<br/>5.2 OptimalMechanisms . . . . . . . . . . . . . . . . . . . . . . 67<br/>5.2.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 67<br/>5.2.2 Solution . . . . . . . . . . . . . . . . . . . . . . . . . 68<br/>5.2.3 Discussion and Interpretation . . . . . . . . . . . . . 71<br/>5.2.4 Auctions versusMechanisms . . . . . . . . . . . . . 75<br/>5.3 EfficientMechanisms . . . . . . . . . . . . . . . . . . . . . . 75<br/>5.3.1 The VCGMechanism . . . . . . . . . . . . . . . . . 76<br/>5.3.2 Budget Balance . . . . . . . . . . . . . . . . . . . . . 78<br/>5.3.3 An Application to Bilateral Trade . . . . . . . . . . 80<br/><strong>6 Auctions with Interdependent Values 83</strong><br/>6.1 The SymmetricModel . . . . . . . . . . . . . . . . . . . . . 86<br/>6.2 Second-Price Auctions . . . . . . . . . . . . . . . . . . . . . 87<br/>6.3 English Auctions . . . . . . . . . . . . . . . . . . . . . . . . 90<br/>6.4 First-Price Auctions . . . . . . . . . . . . . . . . . . . . . . 92<br/>6.5 Revenue Comparisons . . . . . . . . . . . . . . . . . . . . . 96<br/>6.5.1 English versus Second-Price Auctions . . . . . . . . 96<br/>6.5.2 Second-Price versus First-Price Auctions . . . . . . . 97<br/>6.6 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100<br/><strong>7 The Revenue Ranking (“Linkage”) Principle 103</strong><br/>7.1 TheMain Result . . . . . . . . . . . . . . . . . . . . . . . . 103<br/>7.2 Public Information . . . . . . . . . . . . . . . . . . . . . . . 106<br/>7.3 An Alternative Linkage Principle . . . . . . . . . . . . . . . 108<br/><strong>8 Asymmetries and Other Complications 111</strong><br/>8.1 Failures of the Linkage Principle . . . . . . . . . . . . . . . 111<br/>8.2 Asymmetric Equilibria in Symmetric Second-Price Auctions 116<br/>8.3 Asymmetrically Informed Bidders . . . . . . . . . . . . . . . 119<br/>8.4 Reserve Prices and Entry Fees . . . . . . . . . . . . . . . . . 121<br/><strong>9 Efficiency and the English Auction 125</strong><br/>9.1 The Single Crossing Condition . . . . . . . . . . . . . . . . 126<br/>9.2 Two-Bidder Auctions . . . . . . . . . . . . . . . . . . . . . . 127<br/>9.3 The Average Crossing Condition . . . . . . . . . . . . . . . 130<br/>9.4 Three orMore Bidders . . . . . . . . . . . . . . . . . . . . . 131<br/>9.5 Proof of Proposition 9.2 . . . . . . . . . . . . . . . . . . . . 133<br/>9.6 Miscellany . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137<br/><strong>10 Mechanism Design with Interdependent Values 141</strong><br/>10.1 EfficientMechanisms . . . . . . . . . . . . . . . . . . . . . . 142<br/>10.2 OptimalMechanisms . . . . . . . . . . . . . . . . . . . . . . 146<br/><strong>11 Bidding Rings 151</strong><br/>11.1 Collusion in Second-Price Auctions . . . . . . . . . . . . . . 152<br/>11.1.1 Efficient Collusion . . . . . . . . . . . . . . . . . . . 154<br/>11.1.2 Reserve Prices in the Face of Collusion . . . . . . . . 158<br/>11.2 Collusion in First-Price Auctions . . . . . . . . . . . . . . . 160<br/><strong>II Multiple Object Auctions 163<br/>12 An Introduction to Multiple Object Auctions 165</strong><br/>12.1 Sealed-Bid Auctions for Selling Identical Units . . . . . . . 166<br/>12.1.1 Discriminatory Auctions . . . . . . . . . . . . . . . . 168<br/>12.1.2 Uniform-Price Auctions . . . . . . . . . . . . . . . . 169<br/>12.1.3 Vickrey Auctions . . . . . . . . . . . . . . . . . . . . 171<br/>12.2 Some Open Auctions . . . . . . . . . . . . . . . . . . . . . . 172<br/>12.2.1 Dutch Auctions . . . . . . . . . . . . . . . . . . . . . 172<br/>12.2.2 English Auctions . . . . . . . . . . . . . . . . . . . . 172<br/>12.2.3 Ausubel Auctions . . . . . . . . . . . . . . . . . . . . 173<br/><strong>13 Equilibrium and Efficiency with Private Values 179<br/></strong>13.1 The BasicModel . . . . . . . . . . . . . . . . . . . . . . . . 179<br/>13.2 Vickrey Auctions . . . . . . . . . . . . . . . . . . . . . . . . 181<br/>13.3 Efficiency inMultiunit Auctions . . . . . . . . . . . . . . . 183<br/>13.4 Uniform-Price Auctions . . . . . . . . . . . . . . . . . . . . 185<br/>13.4.1 Demand Reduction . . . . . . . . . . . . . . . . . . . 187<br/>13.4.2 Single-Unit Demand . . . . . . . . . . . . . . . . . . 190<br/>13.5 Discriminatory Auctions . . . . . . . . . . . . . . . . . . . . 191<br/>13.5.1 Structure of Equilibria . . . . . . . . . . . . . . . . . 192<br/>13.5.2 Single-Unit Demand . . . . . . . . . . . . . . . . . . 195<br/><strong>14 Some Revenue Considerations 199</strong><br/>14.1 Revenue Equivalence in Multiunit Auctions . . . . . . . . . 200<br/>14.2 Revenue Equivalence with Multiunit Demand: An Example 202<br/><strong>15 Sequential Sales 209</strong><br/>15.1 Sequential First-Price Auctions . . . . . . . . . . . . . . . . 209<br/>15.1.1 Two Units . . . . . . . . . . . . . . . . . . . . . . . . 210<br/>15.1.2 More than Two Units . . . . . . . . . . . . . . . . . 213<br/>15.1.3 Equilibrium Bids and Prices . . . . . . . . . . . . . . 216<br/>15.2 Sequential Second-Price Auctions . . . . . . . . . . . . . . . 217<br/>15.2.1 Revenue Equivalence . . . . . . . . . . . . . . . . . . 217<br/>15.2.2 EquilibriumBids . . . . . . . . . . . . . . . . . . . . 218<br/><strong>16 Nonidentical Objects 223</strong><br/>16.1 TheModel . . . . . . . . . . . . . . . . . . . . . . . . . . . 223<br/>16.2 Efficient Allocations . . . . . . . . . . . . . . . . . . . . . . 225<br/>16.3 Substitutes and Complements . . . . . . . . . . . . . . . . . 226<br/>16.4 Bundling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228<br/>16.5 Some Computational Issues . . . . . . . . . . . . . . . . . . 230<br/>16.6 Budget Constraints . . . . . . . . . . . . . . . . . . . . . . . 232<br/><strong>17 Multiple Objects and Interdependent Values 235</strong><br/>17.1 One-Dimensional Signals . . . . . . . . . . . . . . . . . . . . 235<br/>17.1.1 An Efficient DirectMechanism . . . . . . . . . . . . 236<br/>17.1.2 Efficiency via Open Auctions . . . . . . . . . . . . . 240<br/>17.2 Multidimensional Signals . . . . . . . . . . . . . . . . . . . 243<br/>17.2.1 SingleObject . . . . . . . . . . . . . . . . . . . . . . 244<br/>17.2.2 MultipleObjects . . . . . . . . . . . . . . . . . . . . 248<br/><strong>III Appendices 251</strong><br/>A Continuous Distributions 253<br/>B Stochastic Orders 259<br/>C Order Statistics 265<br/>D Affiliated Random Variables 269<br/>E Some Linear Algebra 273<br/>F Games of Incomplete Information 279<br/>G Existence of Equilibrium in First-Price Auctions 283<br/><strong>References 289<br/>Index 299</strong></p>
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