Download or read book Monotone Equilibrium in Multi unit Auctions written by David McAdams and published by . This book was released on 2002 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Correlated Signals Against Monotone Equilibria written by Michael Landsberger and published by . This book was released on 2000 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book On Monotone Strategy Equilibria in Simultaneous Auctions for Complementary Goods written by Matthew L. Gentry and published by . This book was released on 2019 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Bidding Lower with Higher Values in Multi object Auctions written by David McAdams and published by . This book was released on 2002 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book On Monotone Strategy Equilibria in Simultaneous Auctions for Complementary Goods written by Matthew Gentry and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Download or read book On Monotone Strategy Equilibria in Simultaneous Auctions for Complementary Goods written by Matthew Loren Gentry and published by . This book was released on 2017 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Multi unit Auctions with Complementarities written by Wedad Jasmine Elmaghraby and published by . This book was released on 1998 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Equilibria in multi unit auctions written by Michal Břeský and published by . This book was released on 1999 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Pure Equilibrium Strategies in Multi unit Auctions with Private Value Bidders written by Michal Břeský and published by . This book was released on 2008 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Example of Multi unit Auctions with Atypically Many Equilibria written by Richard Engelbrecht-Wiggans and published by . This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Putting Auction Theory to Work written by Paul Milgrom and published by Cambridge University Press. This book was released on 2004-01-12 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Handbook of Econometrics written by James Joseph Heckman and published by Elsevier. This book was released on 2007 with total page 1013 pages. Available in PDF, EPUB and Kindle. Book excerpt: As conceived by the founders of the Econometric Society, econometrics is a field that uses economic theory and statistical methods to address empirical problems in economics. It is a tool for empirical discovery and policy analysis. The chapters in this volume embody this vision and either implement it directly or provide the tools for doing so. This vision is not shared by those who view econometrics as a branch of statistics rather than as a distinct field of knowledge that designs methods of inference from data based on models of human choice ...

Download or read book Multi unit Auctions with Budget constrained Bidders written by Gagan Pratap Ghosh and published by . This book was released on 2012 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Handbook of Game Theory and Industrial Organization Volume I written by Luis C. Corchón and published by Edward Elgar Publishing. This book was released on 2018-02-23 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first volume of this wide-ranging Handbook contains original contributions by world-class specialists. It provides up-to-date surveys of the main game-theoretic tools commonly used to model industrial organization topics. The Handbook covers numerous subjects in detail including, among others, the tools of lattice programming, supermodular and aggregative games, monopolistic competition, horizontal and vertically differentiated good models, dynamic and Stackelberg games, entry games, evolutionary games with adaptive players, asymmetric information, moral hazard, learning and information sharing models.

Download or read book Single Unit Auctions Still Enigmatic written by Michael Landsberger and published by . This book was released on 2000 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the well-known model proposed by Milgrom and Weber in 1982, where players are risk neutral, their valuations are neither private nor common, they depend on privately observed signals and a common, unobservable, random variable S (possibly, multidimensional). We prove that if bidders must entail participation cost, and signals are interdependent, the existing results for single unit auctions are not valid anymore in many cases. In fact, it is not known how many equilibria (if any) exist in such auctions, and how to define (construct, select) the relevant equilibrium. The reason is that in many cases if an equilibrium exists, it can not be supported by monotone (threshold) participation strategies. The driving force of this result is the dual meaning of interdependent signals. When signals are independent, a higher signal is good news. Under dependence, in a monotone equilibrium, a higher signal is both, good and bad news.

Download or read book Handbook of Econometrics written by Zvi Griliches and published by Elsevier. This book was released on 1983 with total page 1013 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook is a definitive reference source and teaching aid for econometricians. It examines models, estimation theory, data analysis and field applications in econometrics.

Download or read book Advances in Economics and Econometrics written by Econometric Society. World Congress and published by Cambridge University Press. This book was released on 2017 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is the first of two volumes containing papers and commentaries presented at the Eleventh World Congress of the Econometric Society, held in Montréal, Canada in August 2015. These papers provide state-of-the-art guides to the most important recent research in economics today. This book includes surveys and interpretations of key developments in economics and econometrics, and discussion of future directions for a wide variety of topics, covering both theory and application. These volumes provide a unique, accessible survey of progress on the discipline, written by leading specialists in their fields. The first volume includes theoretical and applied papers addressing topics such as dynamic mechanism design, agency problems, and networks"--