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We formulate a mean field game where each player stops a privately observed Brownian motion with absorption. Players are ranked according to their level of stopping and rewarded as a function of their relative rank. There is a unique mean…

Optimization and Control · Mathematics 2021-03-09 Marcel Nutz , Yuchong Zhang

This paper studies a variant of the contest model introduced in Seel and Strack [J. Econom. Theory 148 (2013) 2033-2048]. In the Seel-Strack contest, each agent or contestant privately observes a Brownian motion, absorbed at zero, and…

Economics · Quantitative Finance 2016-02-05 Han Feng , David Hobson

This paper discusses the gambling contest introduced in Seel & Strack (Gambling in contests, Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 375, Mar 2012.) and considers the impact of adding a penalty…

Portfolio Management · Quantitative Finance 2013-01-07 Han Feng , David Hobson

We study the design of optimal incentives in sequential processes. To do so, we consider a basic and fundamental model in which an agent initiates a value-creating sequential process through costly investment with random success. If…

Theoretical Economics · Economics 2023-11-22 Jens Gudmundsson , Jens Leth Hougaard , Juan D. Moreno-Ternero , Lars Peter Østerdal

In this paper, we consider the problem of a Principal aiming at designing a reward function for a population of heterogeneous agents. We construct an incentive based on the ranking of the agents, so that a competition among the latter is…

Optimization and Control · Mathematics 2026-04-28 Clémence Alasseur , Erhan Bayraktar , Roxana Dumitrescu , Quentin Jacquet

The problem of reward design examines the interaction between a leader and a follower, where the leader aims to shape the follower's behavior to maximize the leader's payoff by modifying the follower's reward function. Current approaches to…

Optimization and Control · Mathematics 2024-06-10 Shuo Wu , Haoxiang Ma , Jie Fu , Shuo Han

We study tournaments where winning a rank-dependent prize requires passing a minimum performance standard. We show that, for any prize allocation, the optimal standard is always at a mode of performance that is weakly higher than the global…

Theoretical Economics · Economics 2024-12-03 Mikhail Drugov , Dmitry Ryvkin , Jun Zhang

We introduce a mean field game with rank-based reward: competing agents optimize their effort to achieve a goal, are ranked according to their completion time, and paid a reward based on their relative rank. First, we propose a tractable…

Optimization and Control · Mathematics 2017-08-07 Marcel Nutz , Yuchong Zhang

Reward design is a fundamental problem in reinforcement learning (RL). A misspecified or poorly designed reward can result in low sample efficiency and undesired behaviors. In this paper, we propose the idea of programmatic reward design,…

Machine Learning · Computer Science 2022-01-10 Weichao Zhou , Wenchao Li

Reinforcement learning (RL) has shown to be a valuable tool in training neural networks for autonomous motion planning. The application of RL to a specific problem is dependent on a reward signal to quantify how good or bad a certain action…

Robotics · Computer Science 2024-10-28 Benjamin Evans , Herman A. Engelbrecht , Hendrik W. Jordaan

We model learning in a continuous-time Brownian setting where there is prior ambiguity. The associated model of preference values robustness and is time-consistent. It is applied to study optimal learning when the choice between actions can…

Economics · Quantitative Finance 2019-03-06 Larry G. Epstein , Shaolin Ji

Risk measures are commonly used to capture the risk preferences of decision-makers (DMs). The decisions of DMs can be nudged or manipulated when their risk preferences are influenced by factors such as the availability of information about…

Optimization and Control · Mathematics 2023-11-29 Shutian Liu , Quanyan Zhu

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

We study a setting in which a principal selects an agent to execute a collection of tasks according to a specified priority sequence. Agents, however, have their own individual priority sequences according to which they wish to execute the…

Computer Science and Game Theory · Computer Science 2024-10-30 Donya G. Dobakhshari , Lav R. Varshney , Vijay Gupta

We study incentive design when multiple principals simultaneously design mechanisms for their respective teams in environments with strategic spillovers. In this environment, each principal's set of incentive-compatible mechanisms--those…

Theoretical Economics · Economics 2026-05-11 Brian Roberson

Reward design remains a significant bottleneck in applying reinforcement learning (RL) to real-world problems. A popular alternative is reward learning, where reward functions are inferred from human feedback rather than manually specified.…

Machine Learning · Computer Science 2026-01-16 Chaitanya Kharyal , Calarina Muslimani , Matthew E. Taylor

Strategic classification studies the design of a classifier robust to the manipulation of input by strategic individuals. However, the existing literature does not consider the effect of competition among individuals as induced by the…

Computer Science and Game Theory · Computer Science 2022-02-23 Lydia T. Liu , Nikhil Garg , Christian Borgs

Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value} of the stopped variable under the rule optimal…

Probability · Mathematics 2019-07-10 Alexander Gnedin , Alexander Iksanov

Many real-life decisions involve both perceptual processes and weighing the consequences of different actions. However, the neural mechanisms underlying perceptual decisions have typically been examined separately from those underlying…

Neurons and Cognition · Quantitative Biology 2025-02-07 Xiaoyue Zhu , Jeffrey C. Erlich

This paper investigates the so-called reward-balancing methods, a novel class of algorithms for solving discounted-return reinforcement learning (RL) problems. These methods consist of iteratively adjusting the reward function to transform…

Optimization and Control · Mathematics 2026-04-23 Simone Baroncini , Bahman Gharesifard , Giuseppe Notarstefano
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