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Author: Young Wu
Publisher:
ISBN:
Category :
Languages : en
Pages :
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This thesis consists of three chapters. In chapter 1, titled "Design of Committee Search," I apply a mechanism design approach to committee search problems, such as hiring by a department or a couple's search for a house. A special class of simple dynamic decisions rules have agents submit in each period one of three votes: veto, approve, or recommend; the current option is adopted whenever no agent vetoes and at least one agent recommends. I show that every implementable payoff can be attained by randomizing among these simple rules. This result dramatically simplifies the design problem. In chapter 2, titled "School Choice with Observable Characteristics," I study a school choice problem where students have observable characteristics that are correlated with their preferences. For example, one such characteristic may be the location of a student's home, which is correlated with preferences if students tend to prefer nearby schools. I consider mechanisms that are envy-free, efficient, and treat students with the same observable characteristics equally. I show that the welfare-maximizing mechanism in this class is a modified probabilistic serial mechanism with capacities. These capacities specify the maximum number of students with given characteristics that can be admitted into each school. In chapter 3, titled "Mechanism Design for Stopping Problems with Two Actions," I analyse a class of dynamic mechanism design problems in which a single agent privately observes a time-varying state, chooses a stopping time, and upon stopping, chooses between two actions. The principal designs transfers that depend only on the time the agent stops and on the alternative the agent chooses. The analysis provides necessary and sufficient conditions for implementability in this environment. In particular, I show that any stopping rule in which the agent stops the first time the state falls outside of an interval in the state space can be implemented if and only if a pair of monotonicity conditions is satisfied.
Author: Young Wu
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
This thesis consists of three chapters. In chapter 1, titled "Design of Committee Search," I apply a mechanism design approach to committee search problems, such as hiring by a department or a couple's search for a house. A special class of simple dynamic decisions rules have agents submit in each period one of three votes: veto, approve, or recommend; the current option is adopted whenever no agent vetoes and at least one agent recommends. I show that every implementable payoff can be attained by randomizing among these simple rules. This result dramatically simplifies the design problem. In chapter 2, titled "School Choice with Observable Characteristics," I study a school choice problem where students have observable characteristics that are correlated with their preferences. For example, one such characteristic may be the location of a student's home, which is correlated with preferences if students tend to prefer nearby schools. I consider mechanisms that are envy-free, efficient, and treat students with the same observable characteristics equally. I show that the welfare-maximizing mechanism in this class is a modified probabilistic serial mechanism with capacities. These capacities specify the maximum number of students with given characteristics that can be admitted into each school. In chapter 3, titled "Mechanism Design for Stopping Problems with Two Actions," I analyse a class of dynamic mechanism design problems in which a single agent privately observes a time-varying state, chooses a stopping time, and upon stopping, chooses between two actions. The principal designs transfers that depend only on the time the agent stops and on the alternative the agent chooses. The analysis provides necessary and sufficient conditions for implementability in this environment. In particular, I show that any stopping rule in which the agent stops the first time the state falls outside of an interval in the state space can be implemented if and only if a pair of monotonicity conditions is satisfied.
Author: Santiago Balseiro
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Dynamic mechanism design expands the scope of allocations that can be implemented and the performance that can be attained compared to static mechanisms. Even under stringent participation constraints and restrictions on transfers, recent work demonstrated that it is possible for a designer to extract the surplus of all players as revenue when players have quasilinear utilities and the number of interactions is large. Much of the analysis has focused on excludable environments (i.e., any player can be excluded from trade without affecting the utilities of others). The mechanisms presented in the literature, however, do not extend to non-excludable environments. Two prototypical examples of such environments are: (i) public projects, where all players must have the same allocation; and (ii) non-disposable goods, where each item must be allocated to some player. We show a general mechanism that can asymptotically extract full surplus as revenue in such environments. Moreover, we provide a tight characterization for general environments, and identify necessary and sufficient conditions on the possibility of asymptotic full surplus extraction. Our characterization is based on the geometry of achievable utility sets -- convex sets that delineate the expected utilities that can be implemented by static mechanisms. Our results provide a reduction from dynamic to static mechanism design: the geometry of the achievable utility set of static mechanisms completely determines whether it is possible to fully extract surplus in the limit.
Author: Tilman Borgers
Publisher: Oxford University Press
ISBN: 019987588X
Category : Business & Economics
Languages : en
Pages : 263
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Book Description
What is the best way to auction an asset? How should a group of people organize themselves to ensure the best provision of public goods? How should exchanges be organized? In An Introduction to the Theory of Mechanism Design, Tilman Börgers addresses these questions and more through an exploration of the economic theory of mechanism design. Mechanism design is reverse game theory. Whereas game theory takes the rules of the game as a given and makes predictions about the behavior of strategic players, the theory of mechanism design goes a step further and selects the optimal rules of the game. A relatively new economic theory, mechanism design studies the instrument itself as well as the results of the instrument. An Introduction to the Theory of Mechanism Design provides rigorous but accessible explanations of classic results in the theory of mechanism design, such as Myerson's theorem on expected revenue maximizing auctions, Myerson and Satterthwaite's theorem on the impossibility of ex post efficient bilateral trade with asymmetric information, and Gibbard and Satterthwaite's theorem on the non-existence of dominant strategy voting mechanisms. Börgers also provides an examination of the frontiers of current research in the area with an original and unified perspective that will appeal to advanced students of economics.
Author: Dirk Bergemann
Publisher:
ISBN:
Category : Auctions
Languages : en
Pages : 49
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We provide an introduction into the recent developments of dynamic mechanism design with a primary focus on the quasilinear case. First, we describe socially optimal (or efficient) dynamic mechanisms. These mechanisms extend the well known Vickrey-Clark-Groves and D'Aspremont-Gérard-Varet mechanisms to a dynamic environment. Second, we discuss results on revenue optimal mechanism. We cover models of sequential screening and revenue maximizing auctions with dynamically changing bidder types. We also discuss models of information management where the mechanism designer can control (at least partially) the stochastic process governing the agent's types. Third, we consider models with changing populations of agents over time. This allows us to address new issues relating to the properties of payment rules. After discussing related models with risk-averse agents, limited liability, and different performance criteria for the mechanisms, we conclude by discussing a number of open questions and challenges that remain for the theory of dynamic mechanism design.
Author: Santiago Balseiro
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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We consider a principal repeatedly allocating a single resource in each period to one of multiple agents, whose values are private, without relying on monetary payments over an infinite horizon with discounting. We design a dynamic mechanism without monetary transfers, which induces agents to report their values truthfully in each period via promises/threats of future favorable/unfavorable allocations. We show that our mechanism asymptotically achieves the first-best efficient allocation (the welfare-maximizing allocation as if values are public) as agents become more patient and provide sharp characterizations of convergence rates to first best as a function of the discount factor. In particular, in the case of two agents we prove that the convergence rate of our mechanism is optimal, i.e., no other mechanism can converge faster to first best.
Author: Tilman Börgers
Publisher: Oxford University Press, USA
ISBN: 019973402X
Category : Business & Economics
Languages : en
Pages : 263
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Book Description
This book is meant for advanced undergraduate and graduate students of economics who have a good understanding of game theory.
Author: Sham Kakade
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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We consider the problem of designing optimal mechanisms for settings where agents have dynamic private information. We present the Virtual-Pivot Mechanism, that is optimal in a large class of environments that satisfy a separability condition. The mechanism satisfies a rather strong equilibrium notion (it is periodic ex-post incentive compatible and individually rational). We provide both necessary and sufficient conditions for immediate incentive compatibility for mechanisms that satisfy periodic ex-post incentive compatibility in future periods. The result also yields a strikingly simple mechanism for selling a sequence of items to a single buyer. We also show the allocation rule of the Virtual-Pivot Mechanism has a very simple structure (a Virtual Index) in multi-armed bandit settings. Finally, we show through examples that the relaxation technique we use does not produce optimal dynamic mechanisms in general non-separable environments.
Author: Dirk Bergemann
Publisher: World Scientific
ISBN: 981437458X
Category : Business & Economics
Languages : en
Pages : 471
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Book Description
Foreword by Eric Maskin (Nobel Laureate in Economics, 2007)This volume brings together the collected contributions on the theme of robust mechanism design and robust implementation that Dirk Bergemann and Stephen Morris have been working on for the past decade. The collection is preceded by a comprehensive introductory essay, specifically written for this volume with the aim of providing the readers with an overview of the research agenda pursued in the collected papers.The introduction selectively presents the main results of the papers, and attempts to illustrate many of them in terms of a common and canonical example, namely a single unit auction with interdependent values. It is our hope that the use of this example facilitates the presentation of the results and that it brings the main insights within the context of an important economic mechanism, namely the generalized second price auction.
Author: Matthias Doepke
Publisher:
ISBN:
Category :
Languages : en
Pages : 63
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Book Description
We develop general recursive methods to solve for optimal contracts in dynamic principal-agent environments with hidden states and hidden actions. In our baseline model, the principal observes nothing other than transfers. Nevertheless, optimal incentive-constrained insurance can be attained. Starting from a general mechanism with arbitrary communication, randomization, full history dependence, and without restrictions on preferences or technology, we show how the optimal contract can be efficiently implemented as a recursive direct mechanism. Our methods generalize to environments with multiple actions and additional states, some of which may be observable. The key to implementing these extensions is to introduce multiple layers of off-path utility bounds.
Author: Heng Liu
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Book Description
This paper addresses the problem of implementing socially efficient allocations in dynamic environments with interdependent valuations and evolving private information. We construct efficient and incentive compatible dynamic mechanisms, based on the inter-temporal correlation of different agents' private information. Our mechanisms highlight the role of history-dependent transfers, a distinctive feature in dynamic mechanism design. Furthermore, the mechanisms are reminiscent of the classical VCG mechanism, although the latter fails under interdependent valuations. In settings where agents' private information progresses independently, we construct the dynamic counterpart of the generalized VCG mechanism in one-dimensional environments, and provide sufficient conditions for its implementability. These conditions generalize the single-crossing conditions in static problems.
