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Nash`s classical bargaining solution suggests that n players in a non-cooperative bargaining situation should find a solution that maximizes the product of each player's utility functions. We consider a special case: Suppose that the…

Analysis of PDEs · Mathematics 2017-12-21 Micah Warren

Multi-agent systems outperform single agent in complex collaborative tasks. However, in large-scale scenarios, ensuring timely information exchange during decentralized task execution remains a challenge. This work presents an online…

Multiagent Systems · Computer Science 2023-09-07 Junjie Wang , Meng Guo , Zhongkui Li

In this paper we consider a family of optimal control problems for economic models whose state variables are driven by Delay Differential Equations (DDE's). We consider two main examples: an AK model with vintage capital and an advertising…

Optimization and Control · Mathematics 2007-05-23 Giorgio Fabbri , Silvia Faggian , Fausto Gozzi

Multiagent learning settings are inherently more difficult than single-agent learning because each agent interacts with other simultaneously learning agents in a shared environment. An effective approach in multiagent reinforcement learning…

Computer Science and Game Theory · Computer Science 2022-10-31 Dong-Ki Kim , Matthew Riemer , Miao Liu , Jakob N. Foerster , Gerald Tesauro , Jonathan P. How

We analyze conditional optimization problems arising in discrete time Principal-Agent problems of delegated portfolio optimization with linear contracts. Applying tools from Conditional Analysis we show that some results known in the…

Mathematical Finance · Quantitative Finance 2016-06-15 Julio Backhoff , Ulrich Horst

In the study of reactive systems, qualitative properties are usually easier to model and analyze than quantitative properties. This is especially true in systems where mutually beneficial cooperation between agents is possible, such as…

Computer Science and Game Theory · Computer Science 2023-05-18 Senthil Rajasekaran , Suguman Bansal , Moshe Y. Vardi

In this work, we consider the problem of autonomous racing with multiple agents where agents must interact closely and influence each other to compete. We model interactions among agents through a game-theoretical framework and propose an…

Systems and Control · Electrical Eng. & Systems 2023-05-02 Yixuan Jia , Maulik Bhatt , Negar Mehr

We investigate both stationary and time-varying, nonmonotone generalized Nash equilibrium problems that exhibit symmetric interactions among the agents, which are known to be potential. As may happen in practical cases, however, we envision…

Optimization and Control · Mathematics 2024-07-09 Filippo Fabiani , Andrea Simonetto , Paul J. Goulart

An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is…

Optimization and Control · Mathematics 2017-12-29 Hongwei Mei , Jiongmin Yong

Generalized from the concept of consensus, this paper considers a group of edge agreements, i.e. constraints defined for neighboring agents, in which each pair of neighboring agents is required to satisfy one edge agreement constraint. Edge…

Optimization and Control · Mathematics 2023-12-04 Zehui Lu , Shaoshuai Mou

In this paper, we study a time-inconsistent stochastic optimal control problem with a recursive cost functional by a multi-person hierarchical differential game approach. An equilibrium strategy of this problem is constructed and a…

Optimization and Control · Mathematics 2016-06-13 Qingmeng Wei , Jiongmin Yong , Zhiyong Yu

Multi-agent contract design has largely evaluated contracts through the lens of pure Nash equilibria (PNE). This focus, however, is not without loss: In general, the principal can strictly gain by recommending a complex, possibly…

Computer Science and Game Theory · Computer Science 2025-11-25 Paul Dütting , Tomer Ezra , Michal Feldman , Thomas Kesselheim

We study a generic principal-agent problem in continuous time on a finite time horizon. We introduce a framework in which the agent is allowed to employ measure-valued controls and characterise the continuation utility as a solution to a…

Probability · Mathematics 2025-12-01 Daniel Kršek , Dylan Possamaï

In this paper, we consider game problems played by (multi)-integrator agents, subject to external disturbances. We propose Nash equilibrium seeking dynamics based on gradient-play, augmented with a dynamic internal-model based component,…

Optimization and Control · Mathematics 2020-04-10 Andrew R Romano , Lacra Pavel

This paper characterizes differentiable subgame perfect equilibria in a continuous time intertemporal decision optimization problem with non-constant discounting. The equilibrium equation takes two different forms, one of which is…

Optimization and Control · Mathematics 2007-05-23 Ivar Ekeland , Ali Lazrak

We study a multi-agent contracting problem where agents exert costly effort to achieve individually observable binary outcomes. While the principal can theoretically extract the full social welfare using a discriminatory contract that…

Computer Science and Game Theory · Computer Science 2026-02-13 Johannes Brustle , Paul Duetting , Stefano Leonardi , Tomasz Ponitka , Matteo Russo

In this paper, we investigate the distributed optimal control problem for a kind of nonlinear multi-agent systems. In particular,both the state and the system dynamic structures of each agent are private and can only be shared among…

Optimization and Control · Mathematics 2026-04-08 Ruixue Li , Wenjing Yang , Zhaorong Zhang , Xun Li , Juanjuan Xu

We study a finite horizon optimal contracting problem of a risk-neutral principal and a risk-averse agent who receives a stochastic income stream when the agent is unable to make commitments. The problem involves an infinite number of…

Theoretical Economics · Economics 2019-01-14 Junkee Jeon , Hyeng Keun Koo , Kyunghyun Park

A principal uses payments conditioned on stochastic outcomes of a team project to elicit costly effort from the team members. We develop a multi-agent generalization of a classic first-order approach to contract optimization by leveraging…

Theoretical Economics · Economics 2026-03-13 Krishna Dasaratha , Benjamin Golub , Anant Shah

The modelling of modern power markets requires the representation of the following main features: (i) a stochastic dynamic decision process, with uncertainties related to renewable production and fuel costs, among others; and (ii) a…

Optimization and Control · Mathematics 2019-10-10 Joaquim Dias Garcia , Raphael Chabar