Are you excited about how mathematics can be used to describe real-life scenarios? Are you curious to see how game theory plays a role in this? Then join us!

Many real-life problems can be described by a collection of interacting agents making decisions in an uncertain environment. As an example, consider the energy grid, where companies and prosumers (who produce and consume energy at the same time) try to handle the uncertainty coming from renewable sources and demand imbalances. How can the agents take into account this unpredictability to optimize their decision-making process?

The most suitable tool to describe these systems is game theory. A game allows us to model a collection of agents whose “happiness” depends also on the decisions of the other participants. In particular, stochastic Nash equilibrium problems allow to describe the behavior of the agents in presence of uncertainty and to characterize it. One of the main objectives is then to find distributed optimization algorithms which are guaranteed to converge to an equilibrium (i.e., the optimum of each agent, given the actions of the other participants) despite these uncertainties. The goal of this project is to design such algorithms for stochastic Nash equilibrium problems. To achieve this goal, you will use tools from monotone operator theory, stochastic (non-convex) optimization and stochastic programming. The outcome of the proposal will be a characterization of how uncertainty plays a role in Nash equilibrium problems, focusing in particular on distributionally robust Nash equilibrium problems and chance-constraints. Moreover, distributed iterative schemes will be developed with provable convergence guarantees toward the equilibrium.

Job Description
We are looking for a motivated and talented PhD student with a background in the area of Game Theory and Optimization. The successful candidate will be responsible for developing state-of-the-art algorithms that can take into account uncertainties and provide convergence guarantees towards the Nash equilibrium. Your research task will be to propose and validate such algorithms and find suitable application domains for these models. Your work will advance the theoretical analysis as well as potentially have a societal impact via its possible applications.

Your responsibilities will include:

• To perform scientific research in algorithmic game theory and its applications.
• To be able to work independently, as well as collaboratively in both research oriented and in applied settings.
• To publish the main results in top-tier (international) conferences and in international journals.
• To assist with educational tasks, e.g., in tutorial sessions and in supervising students and internships.

Requirements

1. M.Sc. degree (completed, or to be completed shortly) in (Applied) Mathematics, Econometrics, Operations Research, Computing Sciences, Artificial Intelligence or closely related fields. Candidates with a strong academic background and industry experience will also be considered.
2. Demonstrated (e.g., through publications, code, projects, etc.) interest and experience with game theory and/or optimization.
3. Proficiency in English (oral and written).
4. Excellent communication skills.

Additionally, we would like it if you have:

• Experience with programming (Matlab)
• Experience with machine learning.

If your profile does not completely meet the above criteria, but you are interested and you want to show us your unique perspective on why you would fit this project, we would still like to hear from you.

What we offer
As Phd Candidate at Faculty of Science & Engineering, you will be employed by the most international university in the Netherlands, located in the beautiful city of Maastricht. In addition, we offer you:

• Good employment conditions. The position is graded in scale P according to UFO profile PhD Candidate, with corresponding salary based on experience ranging from €2770,00 and €3539,00 gross per month (based on a full-time employment of 38 hours per week). In addition to the monthly salary, an 8.0% holiday allowance and an 8.3% year-end bonus apply.
• An employment contract for a period of 12 months with a scope of 1,0 FTE. Upon a positive evaluation, an extension of 3 years will follow.
• At Maastricht University, the well-being of our employees is of utmost importance, we offer flexible working hours and the possibility to work partly from home if the nature of your position allows it. You will receive a monthly commuting and internet allowance for this. If you work full-time, you will be entitled to 29 vacation days and 4 additional public holidays per year, namely carnival Monday, carnival Tuesday, Good Friday, and Liberation Day. If you choose to accumulate compensation hours, an additional 12 days will be added. Furthermore, you can personalize your employment conditions through a collective labor agreement (CAO) choice model.
• As Maastricht University, we offer various other excellent secondary employment conditions. These include a good pension scheme with the ABP and the opportunity for UM employees to participate in company fitness and make use of the extensive sports facilities that we also offer to our students.
• Last but certainly not least, we provide the space and facilities for your personal and professional development. We facilitate this by offering a wide range of training programs and supporting various well-established initiatives such as 'acknowledge and appreciate'.
  The terms of employment at Maastricht University are largely set out in the collective labor agreement of Dutch Universities. In addition, local provisions specific to UM apply. For more information, click here.

Maastricht University
Why work at Maastricht University?
At Maastricht University (UM), everything revolves around the future. The future of our students, as we work to equip them with a solid, broad-based foundation for the rest of their lives. And the future of society, as we seek solutions through our research to issues from all around the world. Our six faculties combined provide a comprehensive package of study programmes and research.

In our teaching, we use the Problem-Based Learning (PBL) method. Students work in small groups, looking for solutions to problems themselves. By discussing issues and working together to draw conclusions, formulate answers and present them to their peers, students develop essential skills for their future careers.

With over 22,300 students and more than 5,000 employees from all over the world, UM is home to a vibrant and inspiring international community.

Are you drawn to an international setting focused on education, science and scholarship? Are you keen to contribute however your skills and qualities allow? Our door is open to you! As a young European university, we value your talent and look forward to creating the future together.

Click here for more information about UM.

Faculty of Science and Engineering
At the Faculty of Science and Engineering (FSE), we focus on themes such as circularity and sustainability, future farming, digitisation and (scientific) instrument development. FSE's leading projects, like the Einstein Telescope Pathfinder, are sure to grab anyone's attention. The faculty is a vibrant hub of education and research in Science, Technology, Engineering, and Mathematics (STEM) and Liberal Arts and Sciences (LAS). At FSE, over 450 staff members and 3700 students gather to explore e exciting interdisciplinary research and educational programmes. Feel welcome, be part of our team and put your brilliant mind to work!

FSE at the Brightlands Campuses

Maastricht, Sittard-Geleen, Heerlen, and Venlo, the home of four creative Brightlands campuses, are bustling with 30,000 entrepreneurs, researchers, and students working diligently to solve global challenges. The Faculty of Science and Engineering is active on all four Brightlands campuses, and this is where our impact reaches its peak. To give you an idea of what is happening at each campus: Sittard-Geleen is home to the largest chemical site in the Euregion, while Venlo is a large hub for agri-food innovation. Maastricht is the site of the Health Campus, and Heerlen is the place to be for Smart Services.

Department of Advanced Computing Sciences
The Department of Advanced Computing Sciences is Maastricht University’s largest and oldest department broadly covering the fields of artificial intelligence, data science, computer science, mathematics and robotics.

Over 100 researchers work and study in the Department of Advanced Computing Sciences, whose roots trace back to 1987. The department’s staff teaches more than 1,200 bachelor’s and master’s students in 4 specialized study programmes in Data Science, Artificial Intelligence and Computer Science.

Curious?
Are you interested in this exciting position but still have questions? Feel free to contact Barbara Franci, Assistant Professor, via b.franci@maastrichtuniversity.nl for more information.

Applying?
Or are you already convinced and ready to become our new PhD Candidate? Apply now, no later than 19 May, for this position.

To apply for the position, submit the following documents:

• cover letter (1 page max), which includes a motivation of your interest in the vacancy and an explanation of why you would fit well for the PhD position;
• a detailed curriculum vitae;
• a course list of your Masters and Bachelor programs (including grades);
• results of a recent English language test, or other evidence of your English language capabilities;
• name and contact information of two references

The vacancy is open for internal and external candidates. In case of equal qualifications, internal candidates will be prioritized.

Maastricht University is committed to promoting and nurturing a diverse and inclusive community. We believe that diversity in our staff and student population contributes to the quality of research and education at UM, and strive to enable this through inclusive policies and innovative projects led by teams of staff and students. We encourage you to apply for this position.