Discussion Paper No. 93
November 4, 2021
Deterministic versus Stochastic Contracts in a Dynamic Principal-Agent Model
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I show that deterministic dynamic contracts between a principal and an agent are always at least as profitable to the principal as stochastic ones, if the so-called first-order approach in dynamic mechanism design is satisfied. The principal commits, while the agent's type evolution follows a Markov process. My results demonstrate, even when allowing for potential correlation of stochastic contracts across periods that the usual restriction in the literature to deterministic contracts is admissible, as long as the first-order approach is valid.
Keywords:
contract theory; principal-agent theory; dynamic contracting;
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Discussion Paper No. 92
Efficient Implementation with Interdependent Valuations and Maxmin Agents
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We consider a single object allocation problem with multidimensional signals and interdependent valuations. When agents' signals are statistically independent, Jehiel and Moldovanu [Efficient design with interdependent valuations, Econometrica, 69(5):1237-1259, 2001] show that efficient and Bayesian incentive compatible mechanisms generally do not exist. In this paper, we extend the standard model to accommodate maxmin agents and obtain necessary as well as sufficient conditions under which efficient allocations can be implemented. In particular, we derive a condition that quantifies the amount of ambiguity necessary for efficient implementation. We further show that under some natural assumptions on the preferences, this necessary amount of ambiguity becomes sufficient. Finally, we provide a definition of informational size such that given any nontrivial amount of ambiguity, efficient allocations can be implemented if agents are sufficiently informationally small.
Keywords:
efficient implementation; ambiguity aversion; multidimensional signal; interdependent valuation;
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Discussion Paper No. 74
A Compact Topology for Sigma-Algebra Convergence
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We propose a sequential topology on the collection of sub-sigma-algebras included in a separable probability space. We prove compactness of the conditional expectations with respect to L2-bounded random variables along sequences of sub-sigma-algebras. The varying index of measurability is captured by a bundle space construction. As a consequence, we establish the compactness of the space of sub-sigma-algebras. The proposed topology preserves independence and is compatible with join and meet operations. Finally, a new application to information economics is discussed.
Keywords:
convergence of sigma-algebras; compactness of sub-sigma-algebras; conditional expectation; fiber bundle; information economics;
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Discussion Paper No. 72
The Term Structure of Sharpe Ratios and Arbitrage-Free Asset Pricing in Continuous Time
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Recent empirical studies suggest a downward sloping term structure of Sharpe ratios. We present a theoretical framework in continuous time that can cope with such a non-flat forward curve of risk prices. The approach departs from an arbitrage-free and incomplete market setting when different pricing measures are possible. Involved pricing measures now depend on the time of evaluation or the maturity of payoffs. This results in a time inconsistent pricing scheme. The dynamics can be captured by a time-delayed backward stochastic Volterra integral equation, which to the best of our knowledge, has not yet been studied.
Keywords:
term structures; sharpe ratio; incomplete markets; asset pricing; time inconsistency; arbitrage; (time-delayed) volterra equations;
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Discussion Paper No. 68
Matching with Waiting Times: The German Entry-Level Labor Market for Lawyers
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We study the allocation of German lawyers to regional courts for legal trainee-ships. Because of excess demand in some regions lawyers often have to wait before being allocated. The currently used "Berlin" mechanism is not weakly Pareto efficient, does not eliminate justified envy and does not respect improvements. We introduce a mechanism based on the matching with contracts literature, using waiting time as the contractual term. The resulting mechanism is strategy-proof, weakly Pareto efficient, eliminates justified envy and respects improvements. We extend our proposed mechanism to allow for a more flexible allocation of positions over time.
Keywords:
D47; D82; C78; H75; I28;
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Discussion Paper No. 67
Privacy and Platform Competition
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We analyze platform competition where user data is collected to improve adtargeting. Considering that users incur privacy costs, we show that the equilibrium level of data provision is distorted and can be inefficiently high or low: if overall competition is weak or if targeting benefits are low, too much private data is collected, and vice-versa. Further, we find that softer competition on either market side leads to more data collection, which implies substitutability between competition policy measures on both market sides. Moreover, if platforms engage in two-sided pricing, data provision is efficient.
Keywords:
ad targeting; platform competition; privacy; user data;
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Discussion Paper No. 65
Strategic Decentralization and the Provision of Global Public Goods
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We study strategic decentralization in the provision of a global public good. A federation, with the aim of maximizing the aggregate utility of its members, may find it advantageous to decentralize the decision-making, so that its members act autonomously to maximize their own utility. If utility is fully transferable within a federation, the larger a federation is or the more sensitive it is to the public good, the more it has incentives to remain centralized. If an overall increase in the sensitivity to the public good induces some federation(s) to decentralize, it may lead to a decrease in the aggregate provision. With non-transferable utility within a federation, those members that are smaller or less sensitive to the public good are more likely to prefer decentralization. Some members within a federation becoming more sensitive to the public good may thus lead to a lower aggregate provision, because the increased heterogeneity of the federation makes it more inclined to decentralize.
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Discussion Paper No. 53
Consumer-Optimal Information Design
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In many trade environments - such as online markets - buyers fully learn their valuation for goods only after contracting. I characterize the buyer-optimal ex-ante information in such environments. Employing a classical sequential screening framework, I find that buyers prefer to remain partially uninformed, since such an information structure induces the seller to set low prices. For the optimal information signal, trade is efficient, and the seller only extracts the static monopoly profit. Further, I fully characterize all possible surplus divisions that can arise in sequential screening for a given prior.
Keywords:
information disclosure; sequential screening; strategic learning; bayesian persuasion; mechanism design;
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Discussion Paper No. 48
November 3, 2021
English versus Vickrey Auctions with Loss Averse Bidders
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Evidence suggests that people evaluate outcomes relative to expectations. I analyze this expectation-based loss aversion [Ko ̋szegi and Rabin (2006, 2009)] in the context of dynamic and static auctions, where the reference point is given by the (endogenous) equilibrium outcome. If agents update their reference point during the auction, the arrival of information crucially affects equilibrium behavior. Consequently, I show that—even with independent private values—the Vickrey auction yields strictly higher revenue than the En- glish auction, violating the well known revenue equivalence. Thus, dynamic loss aversion offers a novel explanation for empirically observed differences between these auction formats.
Keywords:
vickrey auction; english auction; expectation-based loss aversion; revenue equivalence; dynamic loss aversion; personal equilibrium;
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Discussion Paper No. 45
Mechanism Design with Partially Verifiable Information
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In mechanism design with (partially) verifiable information, the revelation principle holds if allocations are modelled as the Cartesian product of outcomes and verifiable information, giving rise to evidence-contingent mechanisms. Consequently, incentive constraints characterize the implementable set. The revelation principle does not hold when an allocation is modelled as only an outcome so that mechanisms are non-contingent. Yet, any outcome implementable by an evidence-contingent mechanism is implementable by a non-contingent mechanism, provided it can both extend and restrict reporting information. A type-independent bad outcome implies the latter property.
Keywords:
revelation principle; mechanism design; verifiable information;
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