B02
Optimal Dynamic Contracting
Discussion Papers

ddd

Discussion Paper No. 332
July 21, 2022

Cooperation, Competition, and Welfare in a Matching Market

Authors:
Bester, Helmut (FU Berlin and HU Berlin)
Sákovics, József (University of the Balearic Islands and University of Edinburgh)
Abstract:
We investigate the welfare effect of increasing competition in an anonymous two-sided matching market, where matched pairs play an infinitely repeated Pris- oner’s Dilemma. Higher matching efficiency is usually considered detrimental as it creates stronger incentives for defection. We point out, however, that a reduction in matching frictions also increases welfare because more agents find themselves in a cooperative relationship. We characterize the conditions for which increasing competition increases overall welfare. In particular, this is always the case when the incentives for defection are high.
Keywords:
cooperation; prisoner's dilemma; competition; welfare; matching; trust building
JEL-Classification:
C72; C73; C78; D6
Download:
Open PDF file  

Discussion Paper No. 329
May 18, 2022

Stochastic Contracts and Subjective Evaluations

Authors:
Lang, Matthias (LMU Munich)
Abstract:
Subjective evaluations are widely used, but call for different contracts from classical moral-hazard settings. Previous literature shows that contracts require payments to third parties. I show that the (implicit) assumption of deterministic contracts makes payments to third parties necessary. This paper studies incentive contracts with stochastic compensation, like payments in stock options or uncertain arbitration procedures. These contracts incentivize employees without the need for payments to third parties. In addition, stochastic contracts can be more efficient and can make the principal better off compared to deterministic contracts. My results also address the puzzle about the prevalence of labor contracts with stochastic compensation.
Keywords:
subjective evaluations; stochastic contracts; stochastic compensation; budget-balanced contracts; moral hazard; subjective performance measures; incentives
JEL-Classification:
D80; J41; J70; J33
Download:
Open PDF file

Discussion Paper No. 327
May 5, 2022

Portfolio Liquidation Games with Self-Exciting Order Flow

Authors:
Fu, Guanxing (The Hing Kong Polytechnic University)
Horst, Ulrich (HU Berlin)
Xia, Xiaonyu (Wenzhou University)
Abstract:
We analyze novel portfolio liquidation games with self-exciting order flow. Both the N-player game and the mean-field game are considered. We assume that players' trading activities have an impact on the dynamics of future market order arrivals thereby generating an additional transient price impact. Given the strategies of her competitors each player solves a mean-field control problem. We characterize open-loop Nash equilibria in both games in terms of a novel mean-field FBSDE system with unknown terminal condition. Under a weak interaction condition we prove that the FBSDE systems have unique solutions. Using a novel sufficient maximum principle that does not require convexity of the cost function we finally prove that the solution of the FBSDE systems do indeed provide open-loop Nash equilibria.
Keywords:
stochastic games; mean-field games; portfolio liquidation; Hawkes process; singular terminal value
Download:
Open PDF file

Discussion Paper No. 324
April 19, 2022

Collective Brand Reputation

Authors:
Nocke, Volker (Mannheim University)
Strausz, Roland (HU Berlin)
Abstract:
We develop a theory of collective brand reputation for markets in which product quality is jointly determined by local and global players. In a repeated game of imperfect public monitoring, we model collective branding as an aggregation of quality signals generated in different markets. Such aggregation yields a beneficial informativeness effect for incentivizing the global player. It however also induces harmful free-riding by local, market-specific players. The resulting tradeoff yields a theory of optimal brand size and revenue sharing that applies to platform markets, franchising, licensing, umbrella branding, and firms with team production.
Keywords:
collective branding; reputation; free-riding; repeated games; imperfect monitoring
Download:
Open PDF file

Discussion Paper No. 301
November 19, 2021

Optimal Non-Linear Pricing with Data-Sensitive Consumers

Authors:
Krähmer, Daniel (University of Bonn)
Strausz, Roland (HU Berlin)
Abstract:
We introduce consumers with intrinsic privacy preferences into the monopolistic non-linear pricing model. Next to classical consumers, there is a share of data-sensitive consumers who incur a privacy cost if their purchase reveals information to the monopolist. The monopolist discriminates between privacy types using privacy mechanisms which consist of a direct mechanism and a privacy option, targeting, respectively, classical and data-sensitive consumers. We show that a privacy mechanism is optimal if privacy costs are large and that it yields classical consumers a higher utility than data-sensitive consumers with the same valuation. If, by contrast, privacy preferences are public information, data-sensitive consumers with a low valuation obtain a strictly higher utility than classical consumers. With public privacy preferences, data-sensitive consumers and the monopolist are better off, whereas classical consumers are worse off. Our results are relevant for policy measures that target the data-awareness of consumers, such as the European GDPR.
Keywords:
optimal non-linear pricing; privacy; monopolistic screening
JEL-Classification:
Download:
Open PDF file

Discussion Paper No. 287
October 18, 2021

Fairness and Competition in a Bilateral Matching Market

Authors:
Bester, Helmut (FU Berlin and HU Berlin)
Abstract:
This paper analyzes fairness and bargaining in a dynamic bilateral matching market. Traders from both sides of the market are pairwise matched to share the gains from trade. The bargaining outcome depends on the traders’ fairness attitudes. In equilibrium fairness matters because of market frictions. But, when these frictions become negligible, the equilibrium approaches the Walrasian com- petitive equilibrium, independently of the traders’ inequity aversion. Fairness may yield a Pareto improvement; but also the contrary is possible. Overall, the market implications of fairness are very different from its effects in isolated bilat- eral bargaining.
Keywords:
fairness; inequity aversion; bargaining; ultimatum game; matching market; search costs; competitive equilibrium
JEL-Classification:
C78; D5; D6; D83; D9
Download:
Open PDF file

Discussion Paper No. 286
October 17, 2021

Signaling versus Auditing

Authors:
Bester, Helmut (FU Berlin)
Lang, Matthias (LMU Munich)
Li, Jianpei (University of International Business and Economics Beijing)
Abstract:
We analyze a competitive labor market in which workers signal their productivities through education à la Spence (1973), and firms have the option of auditing to learn workers’ productivities. Audits are costly and non–contractible. We characterize the trade–offs between signaling by workers and costly auditing by firms. Auditing is always associated with (partial) pooling of worker types, and education is used as a signal only if relatively few workers have low productivity. Our results feature new auditing patterns and explain empirical observations in labor economics like wage differentials and comparative statics of education choices. Our analysis applies also to other signal- ing problems, e.g., the financial structure of firms, warranties, and initial public offerings.
Keywords:
signaling; information acquisition; auditing; wage differentials; wage dispersion
JEL-Classification:
D82; D86
Download:
Open PDF file

Discussion Paper No. 274
January 26, 2021

Portfolio Liquidation under Factor Uncertainty

Author:

Horst, Ulrich (HU Berlin)
Xia, Xiaonyu (HU Berlin)
Zhou, Chao (National University of Singapore)

Abstract:

We study an optimal liquidation problem under the ambiguity with respect to price impact parameters. Our main results show that the value function and the optimal trading strategy can be characterized by the solution to a semi-linear PDE with superlinear gradient, monotone generator and singular terminal value. We also establish an asymptotic analysis of the robust model for small amounts of uncertainty and analyze the effect of robustness on optimal trading strategies and liquidation costs. In particular, in our model ambiguity aversion is observationally equivalent to increased risk aversion. This suggests that ambiguity aversion increases liquidation rates.

Keywords:

stochastic control; uncertainty; portfolio liquidation; singular terminal value; superlinear growth gradient

Download:

Open PDF file

Discussion Paper No. 255
August 25, 2020

Common Information-processing Irrationality as Trade Creator

Author:

Klishchuk, Bogdan (HU Berlin)

Abstract:

We show that a common (identical across investors) irrationality in information processing can be enough to create nontrivial trade, using one of standard partial-equilibrium environments. We can attribute this trade to their common irrationality because we strip the investors and their circumstances of all heterogeneities but purely age (in a sense experience), make investment horizon age-independent, and keep all information complete. The common irrationality in our model takes the form of a somewhat non-Bayesian information processing. The resulting trade between such essentially identical individuals with the very same irrationality in their information processing can also feature different kinds of mispricing.

Download:

Open PDF file

Discussion Paper No. 251
July 23, 2020

Public Good Overprovision by a Manipulative Provider

Author:

Celik, Gorkem (ESSEC Business School)
Shin, Dongsoo (Santa Clara University)
Strausz, Roland (HU Berlin)

Abstract:

We study contracting between a public good provider and users with private valuations of the good. We show that, once the provider extracts the users' private information, she benefits from manipulating the collective information received from all users when communicating with them. We derive conditions under which such manipulation determines the direction of distortions in public good provision. If the provider is non-manipulative, the public good is always underprovided, whereas overprovision occurs with a manipulative provider. With overprovision, not only high-valuation users, but also low-valuation users may obtain positive rents - users may prefer facing a manipulative provider.

Keywords:

information manipulation; public goods

JEL-Classification:

D82; D86; H41

Download:

Open PDF file