skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


This content will become publicly available on September 16, 2026

Title: Optimal contract design via relaxation: application to the problem of brokerage fee for a client with private signal
Abstract In this paper, we show how relaxation techniques can be used to establish the existence of an optimal contract in the presence of information asymmetry. The method we illustrate was initially motivated by the problem of designing optimal brokerage fees, but it does apply to other optimal contract problems in which (i) the agent controls linearly the drift of a diffusion process, (ii) the direct dependence of the principal’s and the agent’s objectives on the strategy of the agent is of a special form, and (iii) the space of admissible contracts is compact. This method is then applied to establish the existence of an optimal brokerage fee in a market model with a private trading signal observed by the broker’s client, but not by the broker.  more » « less
Award ID(s):
2205751
PAR ID:
10640488
Author(s) / Creator(s):
;
Publisher / Repository:
Springer
Date Published:
Journal Name:
Finance and Stochastics
ISSN:
0949-2984
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; (, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)
    Guruswami, Venkatesan (Ed.)
    We study two recent combinatorial contract design models, which highlight different sources of complexity that may arise in contract design, where a principal delegates the execution of a costly project to others. In both settings, the principal cannot observe the choices of the agent(s), only the project’s outcome (success or failure), and incentivizes the agent(s) using a contract, a payment scheme that specifies the payment to the agent(s) upon a project’s success. We present results that resolve open problems and advance our understanding of the computational complexity of both settings. In the multi-agent setting, the project is delegated to a team of agents, where each agent chooses whether or not to exert effort. A success probability function maps any subset of agents who exert effort to a probability of the project’s success. For the family of submodular success probability functions, Dütting et al. [2023] established a poly-time constant factor approximation to the optimal contract, and left open whether this problem admits a PTAS. We answer this question on the negative, by showing that no poly-time algorithm guarantees a better than 0.7-approximation to the optimal contract. For XOS functions, they give a poly-time constant approximation with value and demand queries. We show that with value queries only, one cannot get any constant approximation. In the multi-action setting, the project is delegated to a single agent, who can take any subset of a given set of actions. Here, a success probability function maps any subset of actions to a probability of the project’s success. Dütting et al. [2021a] showed a poly-time algorithm for computing an optimal contract for gross substitutes success probability functions, and showed that the problem is NP-hard for submodular functions. We further strengthen this hardness result by showing that this problem does not admit any constant factor approximation. Furthermore, for the broader class of XOS functions, we establish the hardness of obtaining a n^{-1/2+ε}-approximation for any ε > 0. 
    more » « less
  2. ; ; (, SIAM Journal on Financial Mathematics)
    This paper constructs optimal brokerage contracts for multiple (heterogeneous) clients trading a single asset whose price follows the Almgren-Chriss model. The distinctive features of this work are as follows: (i) the reservation values of the clients are determined endogenously, and (ii) the broker is allowed to not offer a contract to some of the potential clients, thus choosing her portfolio of clients strategically. We find a computationally tractable characterization of the optimal portfolios of clients (up to a digital optimization problem, which can be solved efficiently if the number of potential clients is small) and conduct numerical experiments which illustrate how these portfolios, as well as the equilibrium profits of all market participants, depend on the price impact coefficients. 
    more » « less
  3. ; ; (, AI For Social Good Workshop)
    Trees on farms provide environmental benefits to society and improve agricultural productivity for farmers. We study incentive schemes for afforestation on farms through the lens of contract theory, designing conditional cash transfer schemes that encourage farmers to sustain tree growth. We capture the tree growth process as a Markov chain whose evolution is affected by the agent’s (farmer) actions – e.g., investing costly effort or cutting the tree for firewood. The principal has imperfect information about the agent’s costs and actions taken, and wants to maximize long-run tree survival with minimal payment. We show how to calculate the optimal contract structure in our model: notably, it can involve time-varying payments and may incentivize the agent to join the program but abandon it prematurely. 
    more » « less
  4. ; ; ; (, Proceedings of 25th ACM Conference on Economics and Computation, EC 2024)
    We study a variant of the principal-agent problem in which the principal does not directly observe the outcomes; rather, she gets a signal related to the agent’s action, according to a variable information structure. We provide simple necessary and sufficient conditions for implementability of an action and a utility profile by some information structure and the corresponding optimal contract — for a riskneutral or risk-averse agent, with or without the limited liability assumption. It turns out that the set of implementable utility profiles is characterized by simple thresholds on the utilities. 
    more » « less
  5. ; (, Mathematical Finance)
    ABSTRACT We investigate an infinite‐horizon time‐inconsistent mean‐field game (MFG) in a discrete time setting. We first present a classic equilibrium for the MFG and its associated existence result. This classic equilibrium aligns with the conventional equilibrium concept studied in MFG literature when the context is time‐consistent. Then we demonstrate that while this equilibrium produces an approximate optimal strategy when applied to the related ‐agent games, it does so solely in a precommitment sense. Therefore, it cannot function as a genuinely approximate equilibrium strategy from the perspective of a sophisticated agent within the ‐agent game. To address this limitation, we propose a newconsistentequilibrium concept in both the MFG and the ‐agent game. We show that a consistent equilibrium in the MFG can indeed function as an approximate consistent equilibrium in the ‐agent game. Additionally, we analyze the convergence of consistent equilibria for ‐agent games toward a consistent MFG equilibrium as tends to infinity. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email