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on Contract Theory and Applications |
| By: | Mao Fabrice Djete |
| Abstract: | In this paper, we address three Principal--Agent problems in a moral hazard context and show that they are connected. We start by studying the problem of Principal with multiple Agents in cooperation. The term cooperation is manifested here by the fact that the agents optimize their criteria through Pareto equilibria. We show that as the number of agents tends to infinity, the principal's value function converges to the value function of a McKean--Vlasov control problem. Using the solution to this McKean--Vlasov control problem, we derive a constructive method for obtaining approximately optimal contracts for the principal's problem with multiple agents in cooperation. In a second step, we show that the problem of Principal with multiple Agents turns out to also converge, when the number of agents goes to infinity, towards a new Principal--Agent problem which is the Principal--Agent problem with Mckean--Vlasov dynamics. This is a Principal--Agent problem where the agent--controlled production follows a Mckean-Vlasov dynamics and the contract can depend of the distribution of the production. The value function of the principal in this setting is equivalent to that of the same McKean--Vlasov control problem from the multi--agent scenario. Furthermore, we show that an optimal contract can be constructed from the solution to this McKean--Vlasov control problem. We conclude by discussing, in a simple example, the connection of these problems with the multitask Principal--Agent problem which is a situation when a principal delegates multiple tasks that can be correlated to a single agent. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.15818 |
| By: | Alessandro Dovis; Paolo Martellini |
| Abstract: | This paper studies optimal information disclosure in dynamic insurance economies with income risk in which an incumbent firm acquires more information about a consumer's persistent type than the rest of the market does. We find that if the incumbent can commit to long-term contracts but the consumer can walk away, the optimal disclosure prescribes no information revelation to maximize cross-subsidization. However, if the incumbent lacks commitment, no cross-subsidization of low-income consumers is feasible for any public information disclosure because of adverse selection. We show that partial information disclosure is typically optimal and it aims at implementing intertemporal consumption smoothing between the first period and the high-state in the second period, generating an inverse of the back-loading result in Harris and Holmstrom (1982). Lastly, we show that, without commitment, banning long-term relations can be beneficial to consumers. Our results can be used to analyze the consequences of policy proposals such as open banking and consumer data ownership. |
| JEL: | E0 |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:33051 |
| By: | Kreutz, Julian (Energiewirtschaftliches Institut an der Universitaet zu Koeln (EWI)); Kopp, Jan Hendrik (Energiewirtschaftliches Institut an der Universitaet zu Koeln (EWI)) |
| Abstract: | Climate-neutral hydrogen is set to play a crucial role in decarbonizing Europe by 2050. Yet, assumptions on hydrogen imports vary widely across existing studies — ranging from fully flexible to fixed import volumes — often neglecting the modalities of future hydrogen trade such as long-term contracts (LTC). This paper addresses this gap by investigating the implications of Take-or-Pay (TOP) rates in hydrogen LTCs on a decarbonized European energy system. We employ a numerical model that optimizes generation capacity, storage and infrastructure investment, and dispatch decisions for the European power and hydrogen sector in 2050, explicitly incorporating TOP obligations in hydrogen LTCs. Our findings show that varying TOP-rates induce significant shifts in cost-minimal infrastructure requirements of the energy system.These shifts underscore the necessity to account for the degree of import flexibility in planning assessments for future energy systems relying on hydrogen imports. Additionally, we show that reduced import flexibility imposed by high TOP rates is balanced predominantly by increased hydrogen storage and withdrawal capacity while import capacity decreases. By simulating dispatch decisions for 35 weather years for the energy systems planned with representative weather, we find that systems planned with high TOP-rates exhibit a lower reliability when weather characteristics during operation differ from the planning stage. Yet, the modalities of future hydrogen trade, for example via long-term contracts (LTC), are often neglected and existing research assumes imports to be completely flexible. |
| Keywords: | Energy System Modeling; Hydrogen Infrastructure; Hydrogen Storage; Hydrogen Long-Term-Contracts; Hydrogen and Electricity Markets |
| JEL: | C61 F10 Q27 Q40 Q41 Q48 |
| Date: | 2024–10–29 |
| URL: | https://d.repec.org/n?u=RePEc:ris:ewikln:2024_007 |
| By: | Frech, Maria; Maideu-Morera, Gerard |
| Abstract: | Empirical evidence highlights women’s demand for flexible working hours as a crit-ical cause of the persistent gender disparities in the labor market. We propose a theory of how hidden demand for flexibility drives gendered employment dynamics. We de-velop a dynamic contracting model between an employer and an employee whose time availability is stochastic and unverifiable. We model men and women only to differ in their probability of having low time availability, which we measure in the ATUS. We explore contracts designed specifically for each gender (gender-tailored) and the polar case where a male-tailored contract is given to both men and women. For the latter, we show that contracting frictions endogenously give rise to well-documented gendered labor market outcomes: (i) the divergence and non-convergence of gender earnings differentials over the life-cycle, and (ii) women’s shorter job duration and weaker labor force attachment. |
| Keywords: | Gender wage gap; child penalty; flexible working hours; recursive con-tracts |
| JEL: | J16 J22 J41 D82 |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:129894 |
| By: | Alberto Gennaro; Thibaut Mastrolia |
| Abstract: | We are considering the problem of optimal portfolio delegation between an investor and a portfolio manager under a random default time. We focus on a novel variation of the Principal-Agent problem adapted to this framework. We address the challenge of an uncertain investment horizon caused by an exogenous random default time, after which neither the agent nor the principal can access the market. This uncertainty introduces significant complexities in analyzing the problem, requiring distinct mathematical approaches for two cases: when the random default time falls within the initial time frame [0, T] and when it extends beyond this period. We develop a theoretical framework to model the stochastic dynamics of the investment process, incorporating the random default time. We then analyze the portfolio manager's investment decisions and compensation mechanisms for both scenarios. In the first case, where the default time could be unbounded, we apply traditional results from Backward Stochastic Differential Equations (BSDEs) and control theory to address the agent problem. In the second case, where the default time is within the interval [0, T], the problem becomes more intricate due to the degeneracy of the BSDE's driver. For both scenarios, we demonstrate that the contracting problem can be resolved by examining the existence of solutions to integro-partial Hamilton-Jacobi-Bellman (HJB) equations in both situations. We develop a deep-learning algorithm to solve the problem in high-dimension with no access to the optimizer of the Hamiltonian function. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.13103 |
| By: | Jose Correa; Andres Cristi; Laura Vargas Koch |
| Abstract: | A fundamental economic question is that of designing revenue-maximizing mechanisms in dynamic environments. This paper considers a simple yet compelling market model to tackle this question, where forward-looking buyers arrive at the market over discrete time periods, and a monopolistic seller is endowed with a limited supply of a single good. In the case of i.i.d. and regular valuations for the buyers, Board and Skrzypacz (2016) characterized the optimal mechanism and proved the optimality of posted prices in the continuous-time limit. Our main result considers the limit case of a continuum of buyers, establishing that for arbitrary independent buyers' valuations, posted prices and capacity rationing can implement the optimal anonymous mechanism. Our result departs from the literature in three ways: It does not make any regularity assumptions, it considers the case of general, not necessarily i.i.d., arrivals, and finally, not only posted prices but also capacity rationing takes part in the optimal mechanism. Additionally, if supply is unlimited, we show that the rationing effect vanishes, and the optimal mechanism can be implemented using posted prices only, \`a la Board (2008). |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.11738 |