Time-consistent equilibria in dynamic models with recursive payoffs and behavioral discounting

Balbus, Łukasz; Reffett, Kevin; Woźny, Łukasz

doi:10.1016/j.jet.2022.105493

Cited by 4 publications

(3 citation statements)

References 109 publications

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“…Ma (1991) studies a multiperiod model in which contracts are subject to renegotiations, and the agent's action has a long-term effect. Balbus et al (2022) show the existence of timeconsistent equilibria for dynamic models with generalized discounting. A survey of some of the state of behavioral economics research in contract theory was provided in Kószegi (2014).…”

Section: Introductionmentioning

confidence: 92%

Time‐inconsistent contract theory

Hernández,

Possamaï

2023

Mathematical Finance

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This paper investigates the moral hazard problem in finite horizon with both continuous and lump‐sum payments, involving a time‐inconsistent sophisticated agent and a standard utility maximizer principal: Building upon the so‐called dynamic programming approach in Cvitanić et al. (2018) and the recently available results in Hernández and Possamaï (2023), we present a methodology that covers the previous contracting problem. Our main contribution consists of a characterization of the moral hazard problem faced by the principal. In particular, it shows that under relatively mild technical conditions on the data of the problem, the supremum of the principal's expected utility over a smaller restricted family of contracts is equal to the supremum over all feasible contracts. Nevertheless, this characterization yields, as far as we know, a novel class of control problems that involve the control of a forward Volterra equation via Volterra‐type controls, and infinite‐dimensional stochastic target constraints. Despite the inherent challenges associated with such a problem, we study the solution under three different specifications of utility functions for both the agent and the principal, and draw qualitative implications from the form of the optimal contract. The general case remains the subject of future research. We illustrate some of our results in the context of a project selection contracting problem between an investor and a time‐inconsistent manager.

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Section: Introductionmentioning

confidence: 92%

Time‐inconsistent contract theory

Hernández,

Possamaï

2023

Mathematical Finance

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“…We shall mention another direction in the literature on the time inconsistency issue, see e.g. Balbus-Reffett-Wozny [3], Cetemen-Feng-Urgun [4] 3 , Djehiche-Helgesson [10],…”

Section: Introductionmentioning

confidence: 99%

“…We refer again to[1,20] for endogenous models for R θ t . It will be very interesting to combine our work with those models, and we shall leave it for future research 3. In this work both the principal and the agent have time inconsistent preferences, and they consider certain optimal renegotiation-proof contract.…”

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confidence: 99%

A Dynamic Principal Agent Problem with One-sided Commitment

Zhang¹,

Zhu²

2022

Preprint

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The principal agent problem in the standard literature is typically time inconsistent, in the sense that an optimal contract may not remain optimal if the principal reconsiders the problem at a later time. Such time inconsistency issue becomes highly relevant when one or both parties do not commit to the contract. In this paper we consider a model where the current agent can quit before the expiration date, and then the principal will hire a new agent from the market, possibly with a different type. Both parties are aware of the non-commitment of the agent when considering the contract in the beginning. We shall show that the new dynamic problem is time consistent in certain sense and we characterize the principal's optimal utility through an infinite dimensional system of HJB equations, parametrized with the agent's type. However, the dynamic value function of the principal could be discontinuous on the boundary, and thus it is characterized as the minimum solution of the HJB system.Two interesting observations are worth mentioning. First, we assume there are a family of agents with different types in the market (as often in reality). It is possible that the principal could hire a cheaper agent when the current one quits, and ends up with a larger optimal utility. So, the principal may have the incentive to design a contract to encourage the agent to quit before the expiration date. Next, we assume the agent (and the principal) will bear some cost when he quits. As a consequence, the principal will see only finitely many quittings within the finite contract period.

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A Dynamic Principal-Agent Problem with One-Sided Commitment

Zhang,

Zhu

2024

Mathematics of OR

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In this paper, we consider a principal-agent problem where the agent is allowed to quit by incurring a cost. When the current agent quits the job, the principal will hire a new one, possibly with a different type. We characterize the principal’s dynamic value function, which could be discontinuous at the boundary, as the (unique) minimal solution of an infinite dimensional system of Hamilton-Jacobi-Bellman equations, parameterized by the agent’s type. This dynamic problem is time consistent in a certain sense. Some interesting findings are worth mentioning. First, self-enforcing contracts are typically suboptimal. The principal would rather let the agent quit and hire a new one. Next, the standard contract for a committed agent may also be suboptimal because of the presence of different types of agents in our model. The principal may prefer no commitment from the agent; then, the principal can hire a cheaper one from the market at a later time by designing the contract to induce the current agent to quit. Moreover, because of the cost incurred to the agent, the principal will see only finitely many quittings. Funding: J. Zhang is supported in part by the NSF [Grants DMS-1908665 and DMS-2205972]. Z. Zhu is supported by The Hong Kong University of Science and Technology (Guangzhou) Start-Up Fund [Grant G0101000240] and the Guangzhou-HKUST(GZ) Joint Funding Program [Grant 2024A03J0630].

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Time-consistent equilibria in dynamic models with recursive payoffs and behavioral discounting

Cited by 4 publications

References 109 publications

Time‐inconsistent contract theory

Time‐inconsistent contract theory

A Dynamic Principal Agent Problem with One-sided Commitment

A Dynamic Principal-Agent Problem with One-Sided Commitment

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