Discussion Paper No. 100
November 4, 2021
Sweet Lemons: Mitigating Collusion in Organizations
Author:
Abstract:
This paper shows that the possibility of collusion between an agent and a supervisor imposes no restrictions on the set of implementable social choice functions (SCF) and associated payoff vectors. Any SCF and any payoff profile that are implementable if the supervisor′s information was public is also implementable when this information is private and collusion is possible. To implement a given SCF we propose a one-sided mechanism that endogenously creates private information for the supervisor vis-à-vis the agent, and conditions both players′ payoffs on this endogenous information. We show that in such a mechanism all collusive side-bargaining fails, similar to the trade failure in Akerlof′s (1970) car market and in models of bilateral trade.
Keywords:
mechanism design; collusion; asymmetric information; correlation;
JEL-Classification:
Download:
Discussion Paper No. 98
Persuasion Against Self-Control Problems
Author:
Abstract:
I derive a social planner's optimal information design in an environment with quasi-hyperbolic discounting consumers without commitment. Consumption induces instantaneous utility, but unknown delayed cost. Consumers may or may not acquire additional costless information on the cost parameter. The planner's optimal signal can be interpreted as an incentive compatible consumption recommendation whenever the cost parameter is below some cut-off. Welfare strictly exceeds the one under full information. I characterize distributional conditions under which welfare attains first best.
Keywords:
bayesian persuasion; present bias; hyperbolic discounting; rational inattention;
JEL-Classification:
Download:
Discussion Paper No. 94
Of Restarts and Shutdowns: Dynamic Contracts with Unequal Discounting
Author:
Abstract:
A large supplier (principal) contracts with a small firm (agent) to repeatedly provide working capital in return for payments. The total factor productivity of the agent is private and follows a Markov process. Moreover, the agent is less patient than the principal. We solve for the optimal contract in this environment. Distortions are pervasive and efficiency unattainable. The optimal contract is characterized by two key properties: restart and shutdown, which capture various aspects of contracts offered in the marketplace. The optimal distortions are completely pinned down by the number of low TFP shocks since the last high shock. Once a high shock arrives, the contract loses memory and repeats the same cycle, we call this endogenous resetting feature restart. If ex ante agency frictions are high, the principal commits to not serving the low type, we call this shutdown. The principal prefers a patient agent if the interim agency friction, as measured by the persistence of the private information is large, and she prefers an impatient agent if it is small. Finally, when global incentive constraints bind, we (i) provide the complete recursive solution, and (ii) characterize a simpler incentive compatible contract that is approximately optimal.
Keywords:
JEL-Classification:
Download:
Discussion Paper No. 93
Deterministic versus Stochastic Contracts in a Dynamic Principal-Agent Model
Author:
Abstract:
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;
JEL-Classification:
Download:
Discussion Paper No. 92
Efficient Implementation with Interdependent Valuations and Maxmin Agents
Author:
Abstract:
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;
JEL-Classification:
Download:
Discussion Paper No. 74
A Compact Topology for Sigma-Algebra Convergence
Author:
Abstract:
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;
JEL-Classification:
Download:
Discussion Paper No. 72
The Term Structure of Sharpe Ratios and Arbitrage-Free Asset Pricing in Continuous Time
Author:
Abstract:
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;
JEL-Classification:
Download:
Discussion Paper No. 68
Matching with Waiting Times: The German Entry-Level Labor Market for Lawyers
Author:
Abstract:
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;
JEL-Classification:
Download:
Discussion Paper No. 67
Privacy and Platform Competition
Author:
Abstract:
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;
JEL-Classification:
Download:
Discussion Paper No. 65
Strategic Decentralization and the Provision of Global Public Goods
Author:
Abstract:
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.
Keywords:
JEL-Classification: