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Duarte Gonçalves
Assistant Professor
University College London, Economics
duarte.goncalves@ucl.ac.uk
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PhD Workshop: Topics in Economic Theory 1
2026-27 Term 1

The topics for this course change every year.


Course Description

Many of the most important decisions unfold over time. We study how people make such decisions when faced with uncertainty, limited information, and evolving opportunities.

We focus on three fundamental challenges.
First: stopping. From accepting a job offer to selling a house or ending a search, timing is often the decision itself.
Second: searching. From browsing products to developing a technology, individuals must decide not just when to choose, but need to search for what is feasible.
Third: learning from others. People rarely make decisions in isolation – they observe, imitate, and respond to what others do.
Understanding these dynamics is key to understanding real-world behaviour in a variety of contexts, from product and technology adoption to the diffusion of misinformation.

This course brings together classic and modern models that address these questions, combining theoretical rigour with economic insight. While technically rooted, the emphasis is on understanding how decisions are made – and sometimes mis-made – in a variety of contexts, such as labour markets, online platforms, financial settings, and social environments.

The course will mostly focus on continuous-time models with a wide variety of applications and has two main objectives. First, to develop tools to analyse continuous-time problems, which should be part of the toolkit of any economic theorist, but also those interested in cutting-edge research in macroeconomics (labour search), econometrics (sequential testing), and finance (option pricing). Second, to foster theoretical research and inspire theory-driven applied research by providing an overview of a collection of models spanning multiple topics of interest, in which time is of the essence.

In the final part of the course, students will present and discuss their research ideas. The goal is to spark questions and inspire research.

This course is aimed at PhD students interested in topics and methods, and in theory, behavioural economics, and dynamic decision-making more broadly. A good grasp of probability theory, real analysis and optimisation is assumed. The course is open to students from outside UCL; please send me an email if you are interested.


Meeting Times and Location
Monday, 9:00-11:00. Drayton House, room 321.
Meeting Dates: 5 October – 14 December 2026. No class on 30 November.

Topics (work in progress)
  1. Stopping: when to take action?
    Introduction to continuous-time stochastic processes, Brownian motion, and and stochastic calculus. Itô integration and Itô's lemma, infinitesimal generator, Dynkin's formula, DPP, HJB, optimal stopping.
    Lecture(s): 5, 12 October.
    References: Branco Sun Villas-Boas (2012 MnSc). Oksendal (2003, ch. 1, 3, 4, 7, 10), Pham (2009, ch. 1, 3, 5), Karatzas Shreve (1998).
    Slides. Handouts.
  2. Entry, Exit, and Strategic Entry: when enter (and exit) the market and how does competition affect it?
    Coupled stopping problems, comparative statics via the HJB, scale function, speed measure, Green's function, Dambis-Dubins-Schwarz.
    Lecture(s): 19 October (TBC).
    References: McDonald Siegel (1986 QJE), Dixit (1989 JPE), Dixit Pindyck (1994 ch. 5), Weeds (2002 REStud), Seel Strack (2013 JET).
    Slides. Handouts.
  3. Learning: when is the evidence good enough?
    Filtering, coupling, time change, Girsanov's theorem, Brownian bridge.
    Lecture(s): 26 October (TBC).
    References: Gonçalves (WP), Cripps Gonçalves (WP), Fudenberg Strack Strzalecki (2018 AER). Oksendal (2003 ch. 6, 8), Peskir Shiryaev (2006 ch. II, III).
  4. Controlled Learning: how much effort and attention to allocate?
    Introduction to optimal control. Controlled infinitesimal generator.
    Lecture(s): 2 November (TBC).
    References: Liang Mu Syrgkanis (2022 Ecta), Ke Villas-Boas (2019 JET), Moscarini Smith (2001 Ecta), Morris Strack (WP). Oksendal (2013 ch. 11).
  5. Conflict: how do opposing parties dynamically manage conflict in a stochastic world?
    Introduction to viscosity solutions. Comparison/maximum principle.
    Lecture(s): 9 November (TBC).
    References: Gul Pesendorfer (2012 REStud), Barilla Gonçalves (2024 TE). Crandall Ishii Lions (1992 BullAMS), Pham (2009 ch. 4).
  6. Career Concerns and Reputation: how to manage reputation over time?
    Lecture(s): 16-23 November (TBC).
    References: Holmstrom (1999 REStud), Board Meyer-ter-Vehn (2013 Ecta), Cisternas (2018 AEJMicro), Faingold Sannikov (2011 Ecta).
  7. Moral Hazard and Private Experimentation: how to design incentives in dynamic settings?
    Lecture(s): 23 November (TBC).
    References: Sannikov (2008 REStud), Georgiadis (2015 REStud), McClellan (2022 Ecta).
  8. Project Presentations.
    Lecture(s): 7 and 14 December.
    Presentations by students.
If there is time, we will cover a selection of other topics based on papers using diffusion processes:
And there are a few left-over topics on learning in games from last year: Materials will be posted below as the course progresses. Here is a list of papers; suggestions of papers to be added are welcome!

Paper Presentations
Most weeks, every member of the class will be required to work in a group of at most 3 people to prepare a 15 minute presentation on an assigned paper. One group will be selected at random to give the presentation at the start of the class.


Project Presentations
The project presentations are to be structured as follows: 20min project idea (motivation, model sketch, target results, proof intuition if available); 10min discussion.
7 December 14 December

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