News and events Tilburg University

Theoretical Foundations of Electricity Market Design

Date: Time: To be announced Location: Room T.B.C.

19 - 22 April 2022

Spring School


This course provides a self-contained set of lectures to bring PhD students and practitioners up to speed on electricity market design. The goal is to offer some economic tools and simulation models using elements of game theory, auction theory, and industrial organization that will allow students to understand the basic functioning of modern electricity markets. The course is set up as a one-week intensive series of lectures and tutorials in a hybrid format (online/physical).


The course is targeted at starting PhD students and advanced Master students but welcomes post-docs and other professionals as well (regulators and industry).


The focus of the course is on economic theory and modeling, so participants are expected to be familiar with basic concepts of game theory (such as Nash equilibria and backward induction), some knowledge on differential equations and constrained optimization.

The course is open to students with an engineering or operations research background. They will be provided with preparatory reading material regarding game theory.


The course starts with an introduction of electricity markets, its special characteristics and the bench-mark peak-load pricing model. It then highlights limitations in the form of non-convexities in production costs, the role of reserve markets in the prevention of black-outs and transmission constraints. We then proceed with describing the different products that are typically traded in the European electricity market. The main differences with the U.S. style power markets are highlighted.

Next, some attention is paid to modeling competition in multi-unit markets in the form of Cournot models, Supply Function Equilibria (SFE) and multi-unit auctions. Market power is the ability of firms to set price above marginal cost. We discuss some indicators of market power.

Electrical power is one of the most volatile commodities, and risk management is therefore important. Producers and consumers can sign long-term delivery contracts and trade financial derivatives to manage their risks. If complete financial markets do not exist and firms are risk-averse, then investment decisions will become sub-optimal.

Long-term contracts may reduce the incentives of firms to unilateral abuse market power but might also change the incentives for firms to tacitly collude or exclude entry of potential competitors. We check the effects of multi-stage competition and arbitrage between different time periods.

In the last part of the course, we touch upon capacity markets. Those are government-run procurement markets in which firms receive a payment in return for some investment and availability.

Note that the focus of the course is on economic theory and modeling, although we will occasionally provide some empirical evidence. As part of the course students will be asked to develop simple optimization models with GAMS (or other optimization software of their choice). In one of the tutorials, we would like to run a few economic experiments.


Bert Willems (Tilburg University)

Guest speakers:

Par Holmberg (IFN Stockholm): Supply Function Equilibria and their applications in the electricity market
Silvester van Koten (UJEP University, Prague): Economic experiments in electricity markets


The course will consist of about 15 hours of lectures and 8 hours of tutorials/experiments.

Lecture 1 Basic model: Optimal generation mix & peak load pricing, reserve markets, non-convexities, and overview of the existing markets
Lecture 2 Modeling competition: Supply Function Equilibria, multi-unit auctions, uniform price vs pay-as-bid auctions
Lecture 3 Uncertainty and Transmission Markets: Risk aversion and uncertainty, incentives for innovation, and allocating transmission capacity.
Lecture 4 Competition and multi-stage markets: Commitment and observability, two-stage settlement markets, intertemporal arbitrage. Foreclosure, and tacit collusion
Lecture 5 Capacity markets: regulatory and market failures, capacity remuneration schemes, state aid.

The course will be offered as physical lectures.  If the Dutch government imposes new restrictions due to rising infection rates, and as a result of this the course is not allowed to take place physically, then the course will be offered completely online.

If COVID limitations make it impossible for a student  to be present physically, we will try to offer the main lectures of the course in a hybrid format,  so students follow the course online. We however encourage students to be present as this will allow for better information transmission and networking among PhD students.

Reading Material

Before the course, students will receive some preparatory reading material on the main policies of the European internal energy markets (unbundling, competition, energy efficiency, ETS). This is background knowledge.

Participants without economics background are expected to bring themselves up to date on basics of game theory before the course starts. Reading material will be provided.

A reading list with academic papers will be provided during the course.


If you would like to participate in the course, please submit your CV and a short motivation letter to TILEC ( ) , at the attention of M. van Genk , and Subject : application Spring School, Theoretical Foundations of  Electricity Market Design

There are a limited number of spots, so we encourage early application to increase acceptance rates. We will select based on motivation, and prior knowledge.

The early application deadline is 15 February  2022. We will notify you about acceptance by 1 March 2022.

The late application deadline is 15 March 2022. If there are insufficient places, you might be put on a waiting list.

  Application deadline Notification of acceptance
Early application 15 February 1 March
Late application 15 March 1 April

Students will receive a certificate of attendance of the course signed by the course teacher and the Director of the Graduate School.

If you want to take the course for ECTS credits and receive a course grade, you will have to pass an exam. This exam consists in writing a short research proposal and an oral exam. Students are themselves responsible to ensure that the ECTS points are recognized at their home university.

Registration fee


Early Registration Fee

(Before March 15)

Late Registration Fee

(After March 15)

Academic Fee (without exam)

400 EUR

600 EUR

Academic Fee (with exam)

600 EUR

800 EUR

Industry / Regulator / Government

800 EUR

1000 EUR

Academic fees are only applicable to full-time faculty or full-time graduate students / PhD-students.

Some tuition waivers might be given to students from universities in developing countries. Please indicate whether you apply for a waiver when you apply to the program. Tuition waivers will only be possible for early applications.

Course details

Course load: 3 ECTS or 84 hrs,

Course Code: 230419-M-3

The course is co-organized by the CentER Graduate School of Tilburg School of Economics and Management (Tisem), Tilburg Law and Economics Center (TILEC).


Course fee

The course fee is payable within 14 days after receipt of the invoice. No VAT is charged for this course.


Tilburg University reserves the right to change parts of the course in the event of unforeseen circumstances or recent developments. You will be informed of any changes as soon as possible.


If the Dutch government imposes new restrictions due to rising infection rates, and as a result of this the course is not allowed to take place physically, then the course will be offered completely online.


Cancellation by a course participant needs to take place in writing. If you cancel in writing not later than four weeks before the first course day, the course fee will be refunded. Tilburg University reserves the right to cancel the course if an insufficient number of participants have registered.


The course participant can report any complaints to Tilburg University in writing. The complaint needs to be described in detail. Complaints do not suspend the obligation to pay the course fee. If the complaint is upheld by Tilburg University, the course participant will receive a reduction of the course fee.