Monotone Equilibrium In Multi Unit Auctions
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Monotone Equilibrium In Multi Unit Auctions
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Author : David McAdams
language : en
Publisher:
Release Date : 2002
Monotone Equilibrium In Multi Unit Auctions written by David McAdams and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
In a large class of multi-unit auctions of identical objects that includes the uniform-price, as-bid (or discriminatory), and Vickrey auctions, a Bayesian Nash equilibrium exists in monotone pure strategies whenever there is a finite price / quantity grid and each bidder's interim expected payoff function satisfies single-crossing in own bid and type. A stronger condition, non-decreasing differences in own bid and type, is satisfied in this class of auctions given (a) independent types and (b) risk-neutral bidders with marginal values that are (c) nondecreasing in own type and have (d) non-increasing differences in own type and others' quantities. A key observation behind this analysis is that each bidder's valuation for what he wins is always modular in own bid in any multi-unit auction in which the allocation is determined by market-clearing. This paper also provides the first proof of pure strategy equilibrium existence in the uniform-price auction when bidders have multi-unit demand and values that are not private. Keywords: Autions, Multi-unit Auctions, Uniform-price Auction, Vickrey Auctions Bidders, Bayesian Nash Equilibrium.
Correlated Signals Against Monotone Equilibria
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Author : Michael Landsberger
language : en
Publisher:
Release Date : 2000
Correlated Signals Against Monotone Equilibria written by Michael Landsberger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
We consider symmetric auctions that may be multi-unit, with multi-dimensional bids and correlated multi-dimensional signals. Payment and allocation mechanisms are quite arbitrary. There are n potential bidders and the process of submitting a bid involves cost, which may be random and may vary across bidders. The number of effective bidders is part of an equilibrium. In fact, our model addresses more general games of which auction games are a special case. However, given the importance of auctions in economic theory and their prevalence in reality, they can be considered as a perfect archetype of our model. We prove that if n is sufficiently large and signals behave in a burst mode (which appears to be rather typical under interdependence), there is no equilibrium supported by monotone strategies. Since results obtained in the auction literature rely on monotonicity of strategies, even very basic results, such as existence and uniqueness of a symmetric equilibrium, become open questions, even for single unit first price auctions. We establish some properties of equilibria. They seem very innocuous and yet, they have power in the sense that they are incompatible with monotone strategies.
Bidding Lower With Higher Values In Multi Object Auctions
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Author : David McAdams
language : en
Publisher:
Release Date : 2002
Bidding Lower With Higher Values In Multi Object Auctions written by David McAdams and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
Multi-object auctions differ in an important way from single-object auctions. When bidders have multi-object demand, equilibria can exist in which bids decrease as values increase! Consider a model with n bidders who receive affiliated one-dimensional types t and whose marginal values are non-decreasing in t and strictly increasing in own type ti. In the first-price auction of a single object, all equilibria are monotone (over the range of types that win with positive probability) in that each bidder's equilibrium bid is non-decreasing in type. On the other hand, some or all equilibria may be non-monotone in many multi-object auctions. In particular, examples are provided for the as-bid and uniform-price auctions of identical objects in which (i) some bidder reduces his bids on all units as his type increases in all equilibria and (ii) symmetric bidders all reduce their bids on some units in all equilibria, and for the as-bid auction of non-identical objects in which (iii) bidders have independent types and some bidder reduces his bids on some packages in all equilibria. Fundamentally, this difference in the structure of equilibria is due to the fact that payoffs fail to satisfy strategic complementarity and/or modularity in these multi-object auctions.
On Monotone Strategy Equilibria In Simultaneous Auctions For Complementary Goods
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Author : Matthew L. Gentry
language : en
Publisher:
Release Date : 2019
On Monotone Strategy Equilibria In Simultaneous Auctions For Complementary Goods written by Matthew L. Gentry and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
We explore existence and properties of equilibrium when N ≥ 2 bidders compete for L ≥ 2 objects via simultaneous but separate auctions. Bidders have private combinatorial valuations over all sets of objects they could win, and objects are complements in the sense that these valuations are supermodular in the set of objects won. We provide a novel partial order on types under which best replies are monotone, and demonstrate that Bayesian Nash equilibria which are monotone with respect to this partial order exist on any finite bid lattice. We apply this result to show existence of monotone Bayesian Nash equilibria in continuous bid spaces when a single global bidder competes for L objects against many local bidders who bid for single objects only. We then consider monotone equilibrium with endogenous tiebreaking building on Jackson, Simon, Swinkels and Zame (2002), and demonstrate that these exist in general. These existence results apply to many auction formats, including first-price, second-price, and all-pay.
Multi Unit Auctions With Complementarities
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Author : Wedad Jasmine Elmaghraby
language : en
Publisher:
Release Date : 1998
Multi Unit Auctions With Complementarities written by Wedad Jasmine Elmaghraby and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
On Monotone Strategy Equilibria In Simultaneous Auctions For Complementary Goods
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Author : Matthew Gentry
language : en
Publisher:
Release Date : 2017
On Monotone Strategy Equilibria In Simultaneous Auctions For Complementary Goods written by Matthew Gentry and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Auctions categories.
"We explore existence and properties of equilibrium when N>1 bidders compete for L>1 objects via simultaneous but separate auctions. Bidders have private combinatorial valuations over all sets of objects they could win, and objects are complements in the sense that these valuations are supermodular in the set of objects won. We provide a novel partial order on types under which best replies are monotone, and demonstrate that Bayesian Nash equilibria which are monotone with respect to this partial order exist on any finite bid lattice. We apply this result to show existence of monotone Bayesian Nash equilibria in continuous bid spaces when a single global bidder competes for L objects against many local bidders who bid for single objects only, highlighting the step in this extension which fails with multiple global bidders. We therefore instead consider an alternative equilibrium with endogenous tie-breaking building on Jackson, Simon, Swinkels and Zame (2002), and demonstrate that this exists in general. Finally, we explore efficiency in simultaneous auctions with symmetric bidders, establishing novel sufficient conditions under which inefficiency in expectation approaches zero as the number of bidders increases."--Abstract and publishers website.
On Monotone Strategy Equilibria In Simultaneous Auctions For Complementary Goods
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Author : Matthew Loren Gentry
language : en
Publisher:
Release Date : 2017
On Monotone Strategy Equilibria In Simultaneous Auctions For Complementary Goods written by Matthew Loren Gentry and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Auctions categories.
We explore existence and properties of equilibrium when N>1 bidders compete for L>1 objects via simultaneous but separate auctions. Bidders have private combinatorial valuations over all sets of objects they could win, and objects are complements in the sense that these valuations are supermodular in the set of objects won. We provide a novel partial order on types under which best replies are monotone, and demonstrate that Bayesian Nash equilibria which are monotone with respect to this partial order exist on any finite bid lattice. We apply this result to show existence of monotone Bayesian Nash equilibria in continuous bid spaces when a single global bidder competes for L objects against many local bidders who bid for single objects only, highlighting the step in this extension which fails with multiple global bidders. We therefore instead consider an alternative equilibrium with endogenous tie-breaking building on Jackson, Simon, Swinkels and Zame (2002), and demonstrate that this exists in general. Finally, we explore efficiency in simultaneous auctions with symmetric bidders, establishing novel sufficient conditions under which inefficiency in expectation approaches zero as the number of bidders increases.
Multi Unit Auctions With Budget Constrained Bidders
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Author : Gagan Pratap Ghosh
language : en
Publisher:
Release Date : 2012
Multi Unit Auctions With Budget Constrained Bidders written by Gagan Pratap Ghosh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Auctions categories.
I derive various qualitative features of this equilibrium, among which are: (1) under mild assumptions, there always exist bidder-types who submit unequal bids in equilibrium, (2) the equilibrium is monotonic in the sense that bidders with higher valuations prefer more unequal splits of their budgets than bidders with lower valuations and the same budget-level. With a formal theory in place, I carry out a quantitative exercise, using data from the 1970 OCS auction. I show that the model is able to match many aspects of the data. (1) In the data, the number of tracts bidders submit bids on is positively correlated with budgets (an R2 of 0.84), even though this relationship is non-monotonic; my model is able to capture this non-monotonicity, while producing an R2 of 0.89 (2) In the data, the average number of bids per tract is 8.21; for the model, this number is 10.09. (3) Auction revenue in the data was $1.927 billion; the model produced a mean revenue of $1.944 billion.
Putting Auction Theory To Work
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Author : Paul Milgrom
language : en
Publisher: Cambridge University Press
Release Date : 2004-01-12
Putting Auction Theory To Work written by Paul Milgrom and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-12 with Business & Economics categories.
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.
Pure Equilibrium Strategies In Multi Unit Auctions With Private Value Bidders
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Author : Michal Břeský
language : en
Publisher:
Release Date : 2008
Pure Equilibrium Strategies In Multi Unit Auctions With Private Value Bidders written by Michal Břeský and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.