An Introduction to Auction Theory.
Menezes, Flavio M.
An Introduction to Auction Theory. - 1st ed. - 1 online resource (199 pages)
Intro -- Contents -- 1 Introduction -- 2 Preliminaries -- 2.1 Notation -- 2.2 Bayesian Nash Equilibrium -- 2.3 Auctions as Games -- 2.3.1 What is an Auction? -- 2.3.2 Auction Types -- 2.3.3 Auction as Bayesian Games -- 3 Private Values -- 3.1 The Independent Private Values Model -- 3.1.1 First-price Auctions -- 3.1.2 Second-price Auctions -- 3.1.3 Revenue Equivalence -- 3.1.4 Reserve Prices and Entry Fees -- 3.2 The Correlated Private Values Model -- 3.2.1 Second-price Auction -- 3.2.2 First-price Auction -- 3.2.3 Comparison of Expected Payment -- 3.3 The Effect of Risk Aversion -- 3.3.1 Revenue Comparison -- 3.4 The Discrete Valuation Case -- 3.5 Exercises -- 4 Common Value -- 4.1 An Example with Independent Signals -- 4.1.1 First-price Auction -- 4.1.2 Second-price Auction Example -- 4.2 An Example with Correlated Types -- 4.2.1 First-price Auction -- 4.2.2 Second-price Auction -- 4.3 The Symmetric Model with Two Bidders -- 4.3.1 Second-price Auctions -- 4.3.2 First-price Auctions -- 4.3.3 Revenue Comparison -- 4.4 Exercises -- 5 Affiliated Values -- 5.1 The General Model -- 5.2 Second-price Auctions -- 5.3 First-price Auctions -- 5.4 English Auctions -- 5.5 Expected Revenue Ranking -- 5.6 Exercises -- 6 Mechanism Design -- 6.1 The Revelation Principle -- 6.2 Direct Mechanisms -- 6.3 Revenue Equivalence and the Optimal Auction -- 6.4 Some Extensions -- 6.4.1 Non-monotonic Marginal Valuation -- 6.4.2 Correlated Values -- 6.4.3 Several Objects -- 6.4.4 Common Values Auction -- 6.5 Exercises -- 7 Multiple Objects -- 7.1 Sequential Auctions -- 7.2 Simultaneous Auctions -- 7.2.1 Discriminatory Auctions -- 7.2.2 Uniform price Auctions -- 7.3 Optimal Auction -- 7.4 Exercises -- 8 What is Next? -- 8.1 Distribution Hypotheses in Auction Theory -- A: Probability -- A.1 Probability Spaces -- A.2 Uncountable Sample Space Case -- A.3 Random Variables. A.4 Random Vectors and their Distribution -- A.5 Independence of Random Variables -- A.6 The Distribution of the Maximum of Independent Random Variables -- A.7 The Distribution of the Second Highest Value -- A.8 Mean Value of Random Variables -- A.9 Conditional Probability -- B: Differential Equations -- B.1 The Simplest Differential Equation -- B.2 Integrating Factor -- C: Affiliation -- D: Convexity -- References -- Index of Notations -- Index of Proper Names -- Index -- A -- B -- C -- D -- E -- F -- G -- I -- L -- M -- N -- O -- P -- R -- S -- U -- W.
This step-by-step, self-contained introduction to the theory of auctions allows students and readers with a calculus background to work through all the basic results in auction theory. Readers will work through the basic indepent-private-model, understand the effects of introducing correlation in valuations on equilibrium behaviour and the seller's expected revenue, develop a working knowledge of mechanism design, and be introduced to the theory of multi-object auctions.
9780191534720
Auctions - Mathematical models.
Electronic books.
HF5476 -- .M545 2005eb
381/.17/0151
An Introduction to Auction Theory. - 1st ed. - 1 online resource (199 pages)
Intro -- Contents -- 1 Introduction -- 2 Preliminaries -- 2.1 Notation -- 2.2 Bayesian Nash Equilibrium -- 2.3 Auctions as Games -- 2.3.1 What is an Auction? -- 2.3.2 Auction Types -- 2.3.3 Auction as Bayesian Games -- 3 Private Values -- 3.1 The Independent Private Values Model -- 3.1.1 First-price Auctions -- 3.1.2 Second-price Auctions -- 3.1.3 Revenue Equivalence -- 3.1.4 Reserve Prices and Entry Fees -- 3.2 The Correlated Private Values Model -- 3.2.1 Second-price Auction -- 3.2.2 First-price Auction -- 3.2.3 Comparison of Expected Payment -- 3.3 The Effect of Risk Aversion -- 3.3.1 Revenue Comparison -- 3.4 The Discrete Valuation Case -- 3.5 Exercises -- 4 Common Value -- 4.1 An Example with Independent Signals -- 4.1.1 First-price Auction -- 4.1.2 Second-price Auction Example -- 4.2 An Example with Correlated Types -- 4.2.1 First-price Auction -- 4.2.2 Second-price Auction -- 4.3 The Symmetric Model with Two Bidders -- 4.3.1 Second-price Auctions -- 4.3.2 First-price Auctions -- 4.3.3 Revenue Comparison -- 4.4 Exercises -- 5 Affiliated Values -- 5.1 The General Model -- 5.2 Second-price Auctions -- 5.3 First-price Auctions -- 5.4 English Auctions -- 5.5 Expected Revenue Ranking -- 5.6 Exercises -- 6 Mechanism Design -- 6.1 The Revelation Principle -- 6.2 Direct Mechanisms -- 6.3 Revenue Equivalence and the Optimal Auction -- 6.4 Some Extensions -- 6.4.1 Non-monotonic Marginal Valuation -- 6.4.2 Correlated Values -- 6.4.3 Several Objects -- 6.4.4 Common Values Auction -- 6.5 Exercises -- 7 Multiple Objects -- 7.1 Sequential Auctions -- 7.2 Simultaneous Auctions -- 7.2.1 Discriminatory Auctions -- 7.2.2 Uniform price Auctions -- 7.3 Optimal Auction -- 7.4 Exercises -- 8 What is Next? -- 8.1 Distribution Hypotheses in Auction Theory -- A: Probability -- A.1 Probability Spaces -- A.2 Uncountable Sample Space Case -- A.3 Random Variables. A.4 Random Vectors and their Distribution -- A.5 Independence of Random Variables -- A.6 The Distribution of the Maximum of Independent Random Variables -- A.7 The Distribution of the Second Highest Value -- A.8 Mean Value of Random Variables -- A.9 Conditional Probability -- B: Differential Equations -- B.1 The Simplest Differential Equation -- B.2 Integrating Factor -- C: Affiliation -- D: Convexity -- References -- Index of Notations -- Index of Proper Names -- Index -- A -- B -- C -- D -- E -- F -- G -- I -- L -- M -- N -- O -- P -- R -- S -- U -- W.
This step-by-step, self-contained introduction to the theory of auctions allows students and readers with a calculus background to work through all the basic results in auction theory. Readers will work through the basic indepent-private-model, understand the effects of introducing correlation in valuations on equilibrium behaviour and the seller's expected revenue, develop a working knowledge of mechanism design, and be introduced to the theory of multi-object auctions.
9780191534720
Auctions - Mathematical models.
Electronic books.
HF5476 -- .M545 2005eb
381/.17/0151