Lahr, Patrick: Essays in Theoretical Microeconomics. - Bonn, 2024. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.

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@phdthesis{handle:20.500.11811/11293,

urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-74436,

author = {{Patrick Lahr}},

title = {Essays in Theoretical Microeconomics},

school = {Rheinische Friedrich-Wilhelms-Universität Bonn},

year = 2024,

month = feb,

note = {This thesis comprises three self-contained essays dealing with the communication and use of information between strategic players. In Chapters 1 and 3, I follow the mechanisms design paradigm, assuming that a player (referred to as the principal or designer) can commit to how she uses the information other players (referred to as agents or voters) provide her. In contrast, Chapter 2 aligns with the cheap-talk literature.

Chapter 1 studies a model of delegation in which allocations are lotteries over a finite set of outcomes. The principal uses randomization to screen agents’ von Neumann Morgenstern preferences and I permit the full domain of such preferences. I characterize all mechanisms that cannot be implemented by randomizing over other mechanisms, i.e., the extreme points of the set of mechanisms. A principal who herself maximizes utility in the von Neumann Morgenstern sense does not benefit from random mixing, as her utility is linear, so it is without loss to assume that she always choose an extreme point. It follows that every optimal mechanism using information from the agent must grant him the option to veto one outcome of his choosing. The only other potentially optimal mechanisms are constant and deterministic, dictating an outcome for the agent. A second consequence of this characterization illuminates the complexity of different classes of delegation problems. For instance, the class of problems with at most three different outcomes is simple, while all others are not.

Chapter 2, which is joint work with Justus Winkelmann, discusses a model of advice. In this model, a single decision-maker receives messages from multiple imperfectly informed experts about an unknown state of the world, with binary state and action. We assume that advisors either align with the interests of the decision maker or have state-independent preferences. These assumptions apply to various contexts, such as regulatory proceedings or peer review of research papers. The most informative equilibrium exhibits perfect communication of intermediate signals, but unaligned experts limit the transmission of the best signals. We present the concept of the "fragility of specialization" and show that more information is lost withmore specialized experts. If the likelihood of diverging interests amongexperts is high, communication becomes binary, resembling a voting procedure.

Chapter 3 investigates utilitarian welfare maximization among strategyproof and anonymous mechanism in a social choice model. I focus the question: Is surjectivity, i.e., the requirement that a social choice function must select any possible outcome under some preference profile, restrictive?

In the case decisions between more then three outcomes and considering the full domain of preferences, the answer is affirmative, due to the Gibbard-Satterthwaite theorem. Decisions between two options typically outperform dictatorships. When preferences are single-peaked, and feasible mechanisms satisfy surjectivity, the answer remains positive. However, the most extreme outcomes need not be excluded to maximize welfare. I provide a tight welfare guarantee for surjective mechanisms as a function of the number of possible outcomes. In particular, no fraction of optimal welfare can be guaranteed when the numbers of outcomes is unbounded.},

url = {https://hdl.handle.net/20.500.11811/11293}

}

urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-74436,

author = {{Patrick Lahr}},

title = {Essays in Theoretical Microeconomics},

school = {Rheinische Friedrich-Wilhelms-Universität Bonn},

year = 2024,

month = feb,

note = {This thesis comprises three self-contained essays dealing with the communication and use of information between strategic players. In Chapters 1 and 3, I follow the mechanisms design paradigm, assuming that a player (referred to as the principal or designer) can commit to how she uses the information other players (referred to as agents or voters) provide her. In contrast, Chapter 2 aligns with the cheap-talk literature.

Chapter 1 studies a model of delegation in which allocations are lotteries over a finite set of outcomes. The principal uses randomization to screen agents’ von Neumann Morgenstern preferences and I permit the full domain of such preferences. I characterize all mechanisms that cannot be implemented by randomizing over other mechanisms, i.e., the extreme points of the set of mechanisms. A principal who herself maximizes utility in the von Neumann Morgenstern sense does not benefit from random mixing, as her utility is linear, so it is without loss to assume that she always choose an extreme point. It follows that every optimal mechanism using information from the agent must grant him the option to veto one outcome of his choosing. The only other potentially optimal mechanisms are constant and deterministic, dictating an outcome for the agent. A second consequence of this characterization illuminates the complexity of different classes of delegation problems. For instance, the class of problems with at most three different outcomes is simple, while all others are not.

Chapter 2, which is joint work with Justus Winkelmann, discusses a model of advice. In this model, a single decision-maker receives messages from multiple imperfectly informed experts about an unknown state of the world, with binary state and action. We assume that advisors either align with the interests of the decision maker or have state-independent preferences. These assumptions apply to various contexts, such as regulatory proceedings or peer review of research papers. The most informative equilibrium exhibits perfect communication of intermediate signals, but unaligned experts limit the transmission of the best signals. We present the concept of the "fragility of specialization" and show that more information is lost withmore specialized experts. If the likelihood of diverging interests amongexperts is high, communication becomes binary, resembling a voting procedure.

Chapter 3 investigates utilitarian welfare maximization among strategyproof and anonymous mechanism in a social choice model. I focus the question: Is surjectivity, i.e., the requirement that a social choice function must select any possible outcome under some preference profile, restrictive?

In the case decisions between more then three outcomes and considering the full domain of preferences, the answer is affirmative, due to the Gibbard-Satterthwaite theorem. Decisions between two options typically outperform dictatorships. When preferences are single-peaked, and feasible mechanisms satisfy surjectivity, the answer remains positive. However, the most extreme outcomes need not be excluded to maximize welfare. I provide a tight welfare guarantee for surjective mechanisms as a function of the number of possible outcomes. In particular, no fraction of optimal welfare can be guaranteed when the numbers of outcomes is unbounded.},

url = {https://hdl.handle.net/20.500.11811/11293}

}