Discussion Paper No. 347
November 30, 2022
Correlation-Savvy Sellers
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A multi-product monopolist sells sequentially to a buyer who privately learns his valuations. Using big data, the monopolist learns the intertemporal correlation of the buyer's valuations. Perfect price discrimination is generally unattainable—even when the seller learns the correlation perfectly, has full commitment, and in the limit where the consumption good about which the buyer has ex ante private information becomes insignificant. This impossibility is due to informational externalities which requires information rents for the buyer's later consumption. These rents induce upward and downward distortions, violating the generalized no distortion at the top principle of dynamic mechanism design.
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Discussion Paper No. 332
July 21, 2022
Cooperation, Competition, and Welfare in a Matching Market
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We investigate the welfare effect of increasing competition in an anonymous two-sided matching market, where matched pairs play an infinitely repeated Prisoner’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;
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Discussion Paper No. 329
May 18, 2022
Stochastic Contracts and Subjective Evaluations
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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;
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Discussion Paper No. 327
May 5, 2022
Portfolio Liquidation Games with Self-Exciting Order Flow
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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.
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stochastic games; mean-field games; portfolio liquidation; Hawkes process; singular terminal value;
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Discussion Paper No. 324
April 19, 2022
Collective Brand Reputation
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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;
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Discussion Paper No. 301
November 19, 2021
Optimal Non-Linear Pricing with Data-Sensitive Consumers
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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;
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Discussion Paper No. 287
November 10, 2021
Fairness and Competition in a Bilateral Matching Market
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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.
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fairness; inequity aversion; bargaining; ultimatum game; matching market; search costs; competitive equilibrium;
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Discussion Paper No. 286
Signaling versus Auditing
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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.
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signaling; information acquisition; auditing; wage differentials; wage dispersion;
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Discussion Paper No. 274
Portfolio Liquidation under Factor Uncertainty
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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;
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Discussion Paper No. 255
November 9, 2021
Common Information-processing Irrationality as Trade Creator
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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.
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