'Paul Milgrom has combined fundamental work in economic theory and, in particular, the theory of auctions, with extensive practical participation in the auctions of the electromagnetic spectrum. This book is a brilliant synthesis of his own and others' contributions to the field. The impact of practical problems on the need for theory is thoroughly exemplified. The exposition of the theory has that complete ease only achievable through complete mastery and intense work.' Kenneth Arrow, Nobel Laureate, Stanford University

• Section 1. Getting to Work: 1. Politics sets the stage; 2. Designing for multiple goals; 3. Comparing seller revenues; 4. The academic critics; 5. Plan for this book; Part I. The Mechanism Design Approach; Section 2. Vickrey–Clarke–Groves Mechanisms: 6. Formulation; 7. Always optimal and weakly dominant strategies; 8. Balancing the budget; 9. Uniqueness; 10. Disadvantages of the Vickrey auction; 11. Conclusion; Section 3. The Envelope Theorem and Payoff Equivalence: 12. Hottelling's lemma; 13. The envelope theorem in integral form; 14. Quasi-linear payoffs; 15. Conclusion; Section 4. Bidding Equilibrium and Revenue Differences: 16. The single crossing conditions; 17. Deriving and verifying equilibrium strategies; 18. Revenue comparisons in the benchmark model; 19. Expected-revenue maximizing auctions; 20. Conclusion; Section 5. Interdependence of Types and Values: 21. Which models and assumptions are 'useful'?; 22. Statistical dependence and revenue-maximizing auctions; 23. Wilson's drainage tract model; 24. Correlated types model interdependent values; 25. Conclusion; Section 6. Auctions in Context: 26. The profit and surplus contribution of an entrant; 27. Symmetric models with costly entry; 28. Asymmetric models: devices to promote competition; 29. After the bidding ends; 30. Conclusion; Part II. Multi-Unit Auctions; Section 7. Uniform Price Auctions: 31. Uniform price sealed bid auctions; 32. Simultaneous ascending auctions; 33. Conclusion; Section 8. Package Auctions and Combinatorial Bidding: 34. Vickrey auctions and the monotonicity problems; 35. Bernheim–Whinston first-price package auctions; 36. Ausubel–Milgrom ascending proxy auctions; 37. Conclusion.

'Paul Milgrom has combined fundamental work in economic theory and, in particular, the theory of auctions, with extensive practical participation in the auctions of the electromagnetic spectrum. This book is a brilliant synthesis of his own and others' contributions to the field. The impact of practical problems on the need for theory is thoroughly exemplified. The exposition of the theory has that complete ease only achievable through complete mastery and intense work.' Kenneth Arrow, Nobel Laureate, Stanford University

• Section 1. Getting to Work: 1. Politics sets the stage; 2. Designing for multiple goals; 3. Comparing seller revenues; 4. The academic critics; 5. Plan for this book; Part I. The Mechanism Design Approach; Section 2. Vickrey–Clarke–Groves Mechanisms: 6. Formulation; 7. Always optimal and weakly dominant strategies; 8. Balancing the budget; 9. Uniqueness; 10. Disadvantages of the Vickrey auction; 11. Conclusion; Section 3. The Envelope Theorem and Payoff Equivalence: 12. Hottelling's lemma; 13. The envelope theorem in integral form; 14. Quasi-linear payoffs; 15. Conclusion; Section 4. Bidding Equilibrium and Revenue Differences: 16. The single crossing conditions; 17. Deriving and verifying equilibrium strategies; 18. Revenue comparisons in the benchmark model; 19. Expected-revenue maximizing auctions; 20. Conclusion; Section 5. Interdependence of Types and Values: 21. Which models and assumptions are 'useful'?; 22. Statistical dependence and revenue-maximizing auctions; 23. Wilson's drainage tract model; 24. Correlated types model interdependent values; 25. Conclusion; Section 6. Auctions in Context: 26. The profit and surplus contribution of an entrant; 27. Symmetric models with costly entry; 28. Asymmetric models: devices to promote competition; 29. After the bidding ends; 30. Conclusion; Part II. Multi-Unit Auctions; Section 7. Uniform Price Auctions: 31. Uniform price sealed bid auctions; 32. Simultaneous ascending auctions; 33. Conclusion; Section 8. Package Auctions and Combinatorial Bidding: 34. Vickrey auctions and the monotonicity problems; 35. Bernheim–Whinston first-price package auctions; 36. Ausubel–Milgrom ascending proxy auctions; 37. Conclusion.

'Paul Milgrom has combined fundamental work in economic theory and, in particular, the theory of auctions, with extensive practical participation in the auctions of the electromagnetic spectrum. This book is a brilliant synthesis of his own and others' contributions to the field. The impact of practical problems on the need for theory is thoroughly exemplified. The exposition of the theory has that complete ease only achievable through complete mastery and intense work.' Kenneth Arrow, Nobel Laureate, Stanford University

• Section 1. Getting to Work: 1. Politics sets the stage; 2. Designing for multiple goals; 3. Comparing seller revenues; 4. The academic critics; 5. Plan for this book; Part I. The Mechanism Design Approach; Section 2. Vickrey–Clarke–Groves Mechanisms: 6. Formulation; 7. Always optimal and weakly dominant strategies; 8. Balancing the budget; 9. Uniqueness; 10. Disadvantages of the Vickrey auction; 11. Conclusion; Section 3. The Envelope Theorem and Payoff Equivalence: 12. Hottelling's lemma; 13. The envelope theorem in integral form; 14. Quasi-linear payoffs; 15. Conclusion; Section 4. Bidding Equilibrium and Revenue Differences: 16. The single crossing conditions; 17. Deriving and verifying equilibrium strategies; 18. Revenue comparisons in the benchmark model; 19. Expected-revenue maximizing auctions; 20. Conclusion; Section 5. Interdependence of Types and Values: 21. Which models and assumptions are 'useful'?; 22. Statistical dependence and revenue-maximizing auctions; 23. Wilson's drainage tract model; 24. Correlated types model interdependent values; 25. Conclusion; Section 6. Auctions in Context: 26. The profit and surplus contribution of an entrant; 27. Symmetric models with costly entry; 28. Asymmetric models: devices to promote competition; 29. After the bidding ends; 30. Conclusion; Part II. Multi-Unit Auctions; Section 7. Uniform Price Auctions: 31. Uniform price sealed bid auctions; 32. Simultaneous ascending auctions; 33. Conclusion; Section 8. Package Auctions and Combinatorial Bidding: 34. Vickrey auctions and the monotonicity problems; 35. Bernheim–Whinston first-price package auctions; 36. Ausubel–Milgrom ascending proxy auctions; 37. Conclusion.