Pure Strategy Equilibria of Single and Double Auctions with Interdependent Values PDF Download
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Author: Aloisio Araujo
Publisher:
ISBN:
Category :
Languages : en
Pages : 16
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Book Description
We prove the existence of monotonic pure strategy equilibrium for many kinds of asymmetric auctions with n bidders and unitary demands, interdependent values and independent types. The assumptions require monotonicity only in the own bidder's type. The payments can be a function of all bids. Thus, we provide a new equilibrium existence result for asymmetrical double auctions and a small number of bidders. The generality of our setting requires the use of special tie-breaking rules. We present an example of a double auction with interdependent values where all equilibria are trivial, that is, they have zero probability of trade. This is related to Akerlof's “market for lemmons” example and to the “winner's curse,” establishing a connection between them. However, we are able to provide sufficient conditions for non-trivial equilibrium existence.
Author: Aloisio Araujo
Publisher:
ISBN:
Category :
Languages : en
Pages : 16
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Book Description
We prove the existence of monotonic pure strategy equilibrium for many kinds of asymmetric auctions with n bidders and unitary demands, interdependent values and independent types. The assumptions require monotonicity only in the own bidder's type. The payments can be a function of all bids. Thus, we provide a new equilibrium existence result for asymmetrical double auctions and a small number of bidders. The generality of our setting requires the use of special tie-breaking rules. We present an example of a double auction with interdependent values where all equilibria are trivial, that is, they have zero probability of trade. This is related to Akerlof's “market for lemmons” example and to the “winner's curse,” establishing a connection between them. However, we are able to provide sufficient conditions for non-trivial equilibrium existence.
Author: David McAdams
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Every mixed strategy equilibrium is outcome equivalent to a monotone pure strategy equilibrium in asymmetric first-price auctions in which n bidders have affiliated, one-dimensional, atomless types and interdependent values.
Author: Srihari Govindan
Publisher:
ISBN:
Category : Auctions
Languages : en
Pages : 21
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Book Description
Author: Susan Athey
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This paper derives sufficient conditions for a class of games of incomplete information, such as first price auctions, to have pure strategy Nash equilibria (PSNE). The paper treats games between two or more heterogeneous agents, each with private information about his own type (for example, a bidder's value for an object of a firm's marginal cost of production), and the types are drawn from an atomless joint probability distribution which potentially allows for correlation between types. Agents' utility may depend directly on the realizations of other agents' types, as in Milgrom and Weber's (1982) formulation of the "mineral rights" auction. The restriction we consider is that each player's expected payoffs satisfy the following single crossing condition: whenever each opponent uses a nondecreasing strategy (that is, an opponent who has a higher type chooses a higher action), then a player's best response strategy is also nondecreasing in her type. The paper has two main results. The first result shows that, when players are restricted to choose among a finite set of actions (for example, bidding or pricing where the smallest unit is a penny), games where players' objective functions satisfy this single crossing condition will have PSNE. The second result demonstrates that when players' utility functions are continuous, as well as in mineral rights auction games and other games where "winning" creates a discontinuity in payoffs, the existence result can be extended to the case where players choose from a continuum of actions. The paper then applies the theory to several classes of games, providing conditions on utility functions and joint distributions over types under which each class of games satisfies the single crossing condition. In particular, the single crossing condition is shown to hold in all first-price, private value auctions with potentially heterogeneous, risk-averse bidders, with either independent or affiliated values, and with reserve prices which may differ across bidders; mineral rights auctions with two heterogeneous bidders and affiliated values; a class of pricing games with incomplete information about costs; a class of all-pay auction games; and a class of noisy signaling games. Finally, the formulation of the problem introduced in this paper suggests a straightforward algorithm for numerically computing equilibrium bidding strategies in games such as first price auctions, and we present numerical analyses of several auctions under alternative assumptions about the joint distribution of types.
Author: Daniel Friedman
Publisher: Routledge
ISBN: 0429972164
Category : Social Science
Languages : en
Pages : 426
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Book Description
This book focuses on markets organized as double auctions in which both buyers and sellers can submit bids and asks for standardized units of well-defined commodities and securities. It examines evidence from the laboratory and computer simulations.
Author: David McAdams
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
The first-price auction has a unique monotone pure strategy equilibrium when there are n symmetric risk-averse bidders having affiliated types and interdependent values.
Author: David McAdams
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
I study monotonicity of equilibrium strategies in first-price auctions with symmetric bidders, risk-aversion, affiliated types, and interdependent values. I prove that every mixed-strategy equilibrium is outcome equivalent to a monotone pure strategy equilibrium under the priority rule for breaking ties. This provides a missing link to establish uniqueness in Milgrom and Weber (1982)'s general symmetric model. Non-monotone equilibria can exist under the coin-flip rule but they are distinguishable: all non-monotone equilibria have positive probability of ties whereas all monotone equilibria have zero probability of ties. This provides a justification for the standard empirical practice of restricting attention to monotone strategies.
Author: Paul Milgrom
Publisher: Cambridge University Press
ISBN: 1139449168
Category : Business & Economics
Languages : en
Pages : 378
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Book Description
This book provides a comprehensive introduction to modern auction theory and its important new applications. It is written by a leading economic theorist whose suggestions guided the creation of the new spectrum auction designs. Aimed at graduate students and professionals in economics, the book gives the most up-to-date treatments of both traditional theories of 'optimal auctions' and newer theories of multi-unit auctions and package auctions, and shows by example how these theories are used. The analysis explores the limitations of prominent older designs, such as the Vickrey auction design, and evaluates the practical responses to those limitations. It explores the tension between the traditional theory of auctions with a fixed set of bidders, in which the seller seeks to squeeze as much revenue as possible from the fixed set, and the theory of auctions with endogenous entry, in which bidder profits must be respected to encourage participation.
Author: Kim-Sau Chung
Publisher:
ISBN:
Category : Auctions
Languages : en
Pages : 76
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Book Description
Author: Vijay Krishna
Publisher: Academic Press
ISBN: 0080922937
Category : Business & Economics
Languages : en
Pages : 337
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Book Description
Auction Theory, Second Edition improves upon his 2002 bestseller with a new chapter on package and position auctions as well as end-of-chapter questions and chapter notes. Complete proofs and new material about collusion complement Krishna’s ability to reveal the basic facts of each theory in a style that is clear, concise, and easy to follow. With the addition of a solutions manual and other teaching aids, the 2e continues to serve as the doorway to relevant theory for most students doing empirical work on auctions. Focuses on key auction types and serves as the doorway to relevant theory for those doing empirical work on auctions New chapter on combinatorial auctions and new analyses of theory-informed applications New chapter-ending exercises and problems of varying difficulties support and reinforce key points
