Evolutionary Game Theory lab
Ideas for student projects
Past PhD candidates
Jessica Cunningham (defended in September 2021; currently research scientist at Munson Lab, Virginia Tech)
Katharina Schneider (born Schüler, defended in May 2020; currently lecturer at Maastricht University)
Monica Salvioli (defended in November 2020; currently postdoc with me)
Li You (defended in March 2018; currently postdoc at Erasmus Medical Center)
Key research interests
Since September 2021, I am an associate professor and Delft Technology Fellow at Faculty of Technology, Policy and Management at Delft University of Technology. My background is in dynamic game theory, with PhD in Stackelberg evolutionary game theory from Delft Institute of Applied Mathematics. Before receiving the Delft Technology Fellowship and joining Delft University of Technology, I set up and led the Dynamic Game Theory team within the Department of Data Science & Knowledge Engineering, Maastricht University, where I was an associate professor in dynamic game theory.
My core research focuses on both game theory (i.e., mathematical theory of interaction) and utilizing mathematical models that I develop to design personalized treatment protocols, often leading to so-called evolutionary therapies, i.e. therapies that anticipate and steer eco-evolutionary response in the treated disease to achieve treatment goals. My mission is to expand health-related research and education at my current faculty.
In game theory, my main interests lie in dynamic noncooperative game theory (originally especially Stackelberg and inverse Stackelberg games and development of theory of Stackelberg evolutionary games, nowadays any differential games; I even deal with some discrete-time dynamics), optimal control theory, and their application in solving complex problems (e.g. in cancer biology, mathematical biology, swarm robotics, and transport). I have been developing rigorous analytical methods and compare them with results of numerical computations and simulations.
Game theory & Optimal controlMy main expertise lies in noncooperative dynamic game theory, especially in Stackelberg and inverse Stackelberg games. Recently, I have also started to analyze games that include both continuous-time and discrete-time dynamics, the so-called hybrid games. Such games have not been researched before and are a great challenge to solve. Moreover, I am connecting the fields of Stackelberg game theory and evolutionary games, which was not done before.
In optimal control, I am currently focusing on problems that might have nonsmooth and even discontinous solutions of associated Hamilton-Jacobi-Bellman-Isaacs equation. To solve such problems, methods of generalized characteristics and/or viscosity solution approach have to be applied. Known methods have to be often extended/adjusted if the problem of interest has a relatively high dimension.
Game theory in biologyIn mathematical biology, my main focus is solving predator-prey hybrid problems using Stackelberg game theory. I have developed a number of models describing interactions in real-world predator prey systems. These models extended extisting population models, for example by including internal properties of the individuals involved into differential equations describing (dynamically changing) system properties. We could explain behavior observed in nature using our models.
The main case study deals with interactions of phytoseiid mites and their intra-seasonal and inter-seasonal optimal behavior. Currently I am focusing on explaining occurence of cry-wolf plants in tri-trophic systems plant-herbivore-carnivore. Moreover, in the past years I have started (together with collaborators from Maastricht, The University of Illinois in Chicago, and Moffitt Cancer Institute in Tampa) a new and exciting project, which focuses on modeling of tumorigenesis and cancer treatment (especially the so-called evolutionary therapies, which take eco-evolutionary properties of cancer into account, and mathematically can be analyzed by combining Stackelberg and evolutionary game theory).
Recently, I have been also working on number fo new research projects, such as:
Game theory in trafficIn traffic control, I focus on applying dynamic Stackelberg and inverse Stackelberg games to compute the optimal toll which would minimize congestion or maximize profit of the road authority, given the distributed system of drivers minimizing their perceived travel costs.
Here various approaches are considered:
Game theory in roboticsIn robotics, I focus on applying dynamic Stackelberg game theory in controling heterogeneous robotic swarms.
I am always happy to discuss my own and others' research and related topics. Please contact me via email or LinkedIn if you would like to discuss problems related to my work.
Main publicationsI am extremely slow in updating my publication list and adding pdf's, thus feel free to contact me if you are missing some of my publications here or if you want to see the pdf's.
Staňková, K., On Stackelberg and Inverse Stackelberg Games & Their Applications in the Optimal Toll Design Problem, the Energy Markets Liberalization Problem, and in the Theory of
Incentives, Delft University of Technology, the Netherlands, 2009.
Two printings (NGInfra series and TRAIL series): ISBN 978-90-79787-03-6 and ISBN 978-90-5584-111-0.
Journal publications and book chapters
Staňková, K., Olsder, G.J., and Bliemer, M.C.J. Optimal toll design problem solved by the inverse Stackelberg games approach. Urban Transport and the Environment in the 21st Century (C.A. Brebbia, V. Dolezel, eds.), Witpress, Southampton, pp. 871-880, 2006.
Staňková, K., Olsder, G.J. and Bliemer, M.C.J. Comparison of Different Toll Policies in the Dynamic Second-best Optimal Toll Design Problem: Case study on a Three-link network. European Journal of Transport and Infrastructure Research, 9(4), pp. 331-346, 2009.
Staňková, K., Olsder, G.J. and De Schutter, B. On European Electricity Market Liberalization: A Game-Theoretic Approach. Information Systems and Operational Research (INFOR)
journal, 48(4), pp. 267-280, 2010.
link tech.rep.(pdf) BibTeX
Staňková, K. (Spel)theoretiseren in Nederland. Nieuw Archief voor Wiskunde, 12(3), pp. 196-197, 2011. (in Dutch)
Staňková, K. Dynamic Games in the European Electricity Market. Industrial Engineering: Innovative Networks (S.P. Sethi, M. Bogataj, L. Ros-McDonnell, eds.), Springer, chapter 22, pp. 191 - 200, 2012.
Koepsell D.R. and Staňková, K. Non-proliferation regimes: immoral and risky - a game-theoretic approach, International Journal on World Peace, 29(2), pp. 63-83, 2012.
link  pdf BibTeX
Staňková, K., Abate A., and Sabelis, M.W., Irreversible prey diapause as an optimal
strategy of a physiologically extended
Lotka-Volterra model, Journal of Mathematical Biology, 66(4), pp. 767-794, 2013. link tech.rep.(pdf)   BibTeX
Staňková, K., Abate A., and Sabelis, M.W., Intra-seasonal Strategies Based on Energy Budgets in a Dynamic Predator-Prey Game, Annals of International Society of Dynamic Games, February 2013.
Staňková, K., Abate A., and Sabelis, M.W., Buša J., and Yu L., Joining or opting out of a Lotka-Volterra game between predators and prey:
Does the best strategy depend on modeling energy lost and gained?, Interface Focus (Theme issue of the Royal Society Interface), 6(3), 12 pp., January 2014 link)
Staňková, K. and Boudewijn, A. Stackelberg and inverse Stackelberg road
pricing games, Game Theoretic Analysis of Congestion (K. Hausken
and J. Zhuang, Eds.), Series in Reliability Engineering Safety and Security, Springer, accepted in April 2014
Abrudan, M., You, L., Staňková, K., and Thuijsman, F., A game theoretical approach to microbial coexistence, Annals of International Society for Dynamic Games, Vol. 14, pp. 267-282, 2016.
Metz, J.A.J., Staňková, K., and Johansson J., The adaptive dynamics of life histories: From fitness-returns to selection gradients and Pontryagin's maximum principle, Journal of Mathematical Biology 72 (4), pp. 1125-1152, Jan 2016
Ferreira, H.L., Staňková, K., Pecas Lopes, J., Slootweg, J.G., and Kling, W.L., Dual technology energy storage system applied to two complementary electricity markets using a weekly differentiated approach, Journal of Energy Storage, 12, 226-242, 2017.
Schüller, K., Staňková, K., and Thuijsman, F., "Game Theory of Pollution: National Policies and Their International Effects", Games, 8(3), paper 30, 2017.
Brown, J.S. and Staňková, K., "Game theory as a conceptual framework for managing insect pests", Current Opinion in Insect Science, 12, pp. 26-32, 2017.
You, L., Brown, J.S., Thuijsman, F., Cunningham, J.J., Gatenby, R.A., Zhang, J., and Staňková, K., Spatial vs. non-spatial eco-evolutionary dynamics in a tumor growth model, Journal of Theoretical Biology, 435, pp. 78-97, December 2017.
Bayer, P., Brown, J.S., and Staňková, K., A Two-Phenotype Model of Immune Evasion by Cancer Cells, Journal of Theoretical Biology, 455, pp. 191-204, July 2018.
Cunningham, J.J., Brown, J.S., Gatenby, R.A. and Staňková, K., 2018. Optimal Control to Develop Therapeutic Strategies for Metastatic Castrate Resistant Prostate Cancer. Journal of Theoretical Biology, 459, pp. 67-78 doi: 10.1016/j.jtbi.2018.09.022
You, L., Knobloch, von, M., Lopez, T., Peschen, V., Radcliffe, S., Koshy Sam, P., Thuijsman, F., Staňková, K. and Brown, J.S., 2019. Including Blood Vasculature into a Game-Theoretic Model of Cancer Dynamics, Games, 10(1), paper 13
Staňková, K., Brown, J.S., Dalton, W.S., and Gatenby, R.A., Optimizing Cancer Treatment Using Game Theory, JAMA Oncology, 5(1), pp. 96-103, January 2019.
Staňková, K., Resistance Games, Nature Ecology & Evolution, February 2019.
Cunningham,J.J., Thuijsman, F., Peeters, R., Viossat, Y., Brown, J.S., Gatenby, R.A. and Staňková, K., Optimal control to reach eco-evolutionary stability in metastatic castrate-resistant prostate cancer, Plos One, December 2020.
Dujon, A.M., Aktipis, A., Alix-Panabieres, C., Amend, S.R., Boddy, A.M., Brown, J.S., Capp, J.-P., DeGregori, J., Ewald, P., Gatenby, R., Gerlinger, M., Giraudeau, M., Hamede, R.K., Hansen, E., Kareva, I., Maley, C.C., Marusyk, A., McGranahan, N., Metzger, M.J., Nedelcu, A.M., Noble, R., Nunney, L., Pienta, K.J., Polyak, K., Pujol, P., Read, A.F., Roche, B., Sebens, S., Solary, E., Staňkov, K., Swain Ewald, H., Thomas, F. and Ujvari, B. (2021), Identifying key questions in the ecology and evolution of cancer. Evolutionary Applications. Accepted Author Manuscript, December 2020.
Salvioli, M., Dubbeldam, Staňková, K. and Brown, J.S., Fisheries management as a Stackelberg Evolutionary Game: Finding an evolutionarily enlightened strategy, Plos One, January 2021.
Staňková, K. and Olsder, G.J. Inverse Stackelberg games versus principal-agent model theory. In Proceedings of the International Symposium on Dynamic Games and Applications, Sophia Antipolis, France. 2006. extended abstract
Staňková, K., Olsder, G.J. and Bliemer, M.C.J. Stackelberg versus inverse Stackelberg games in the dynamic bilevel optimal toll design problem: Which approach provides more efficient tolling?. Selected papers of 9th TRAIL Congress, TRAIL in motion, pp. 263-278, Rotterdam, The Netherlands. 2006. pdf
Staňková, K., Olsder, G.J. and Bliemer, M.C.J. Inverse Stackelberg games and their application to dynamic bilevel optimal toll design problem. In Proceedings of the International Symposium on Dynamic Games and Applications, Sophia Antipolis, France. 2006.
Staňková, K., Stackelberg and Inverse Stackelberg games applied to the optimal toll design problem with reliability-based user equilibrium. In Proceedings of the Infrastructure Reliability Seminar, Delft, The Netherlands. 2006.
Staňková, K., Mettenheim, H.J. and Olsder, G.J. Dynamic optimal toll design problem with second-best-flow-dependent tolling solved using neural networks.In Proceedings of the 10th International Conference on Application of Advanced Technologies in Transportation, Athens, Greece. 2008. pdf
Staňková, K., Bliemer, M.C.J., and Olsder, G.J. Dynamic road pricing with traffic-flow. dependent tolling. In Proceedings of the 87th Annual Meeting of the Transportation Research Board, Washington, D.C., USA, 2008. pdf
Staňková, K., Olsder, G.J. and Bliemer, M.C.J. Solving the dynamic optimal toll design problem with second-best-flow-dependent tolling: Neural Networks Approach.In Proceedings of the 10th TRAIL Congress, Rotterdam, The Netherlands. 2008. pdf
Staňková, K. On Dynamic Optimal Toll Design Problem with Traffic-flow Dependent Tolls and Drivers' Joint Route and Departure Time Choices. In Proceedings of the 19th IEEE International Conference on Control Applications (CCA 2009), St. Petersburg, Russia, 2009. pdf
Staňková, K. and De Schutter, B. First steps towards finding a solution of a dynamic investor-bank game. In Proceedings of the 19th IEEE International Conference on Control Applications (CCA 2010), Yokohama, Japan, 2010. pdf
Staňková, K. and De Schutter, B. On freeway traffic density estimation for a jump Markov linear model based on Daganzo's cell transmission model. Proceedings of the 13th International IEEE Annual Conference on Intelligent Transportation Systems, Funchal, Portugal, 2010. pdf (report version)
Staňková, K. and De Schutter, B. Stackelberg equilibria for discrete-time dynamic games - part I: Deterministic games. Proceedings of the 8th IEEE International Conference on Networking, Sensing & Control (ICNSC 2011), Delft, The Netherlands, 2011. pdf
Staňková, K. and De Schutter, B. Stackelberg equilibria for discrete-time dynamic games - part II: Stochastic games with deterministic information structure. Proceedings of the 8th IEEE International Conference on Networking, Sensing & Control (ICNSC 2011), Delft, The Netherlands, 2011. pdf
Valencia F., Espinosa, J., De Schutter, B. and Staňková, K. Feasible-cooperation distributed model predictive control scheme based on game theory. Proceedings of the 8th IFAC World Congress, Milan, Italy, pp. 386-391, 2011. pdf
Staňková, K., Ranjbar-Sahraei, B., Weiss, G. and Tuyls, K. StaCo: Stackelberg-based Coverage Approach in Robotic Swarms. Proceedings of the Fifth International Conference on Adaptive and Self-Adaptive Systems and Applications (ADAPTIVE 2013), pp. 71-76, Valencia, Spain, May 2013. pdf (report version)
Ranjbar-Sahraei, B., Staňková, K., Weiss, G. and Tuyls, K.Stackelberg-based Coverage Approach in Nonconvex Environments. Proceedings of the12th European Conference on Artificial Life (ECAL), Taormina, Italy, 8 pp., June 2013, link
Ranjbar-Sahraei, B., Alers, S., Staňková, K., Tuyls, K. and Weiss, G. Toward Soft Heterogeneity in Robotic Swarms. Proceedings of the 25th Benelux Conference on Artifficial Intelligence (BNAIC 2013), Delft, The Netherlands, pp. 384-385, November 2013, pdf (report version)
Ferreira, H.L., Gibescu, M., Staňková, K., Kling, W.L., and Lopes, J. P. Dual technology energy storage system applied to two complementary Dutch energy markets, Proceedings of the 12th International Conference on the European Energy Markets, Lisbon, Portugal, pp. 1-5, May 2015.
Some of the abstracts presented at conferences
Staňková, K., Abate, A., and Sabelis, M.W. Studies of Differential Game Based on Physiologically Extended Lotka-Volterra Model, 15th Symposium on Dynamic Games and Applications, Chateau Liblice, Czech Republic, 2012.
Staňková, K., Abate, A., and Sabelis, M.W. Recent outcomes of the Stackelberg game describing interactions between predatory and prey mites, 12th Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics, Vienna, Austria, 2012.
Staňková, K. and Abate, A. On predator-prey continuous time games, Eight International ISDG Workshop, Padova, Italy, 2011.
Staňková, K. and Olsder, G.J. (Inverse) Stackelberg Game in an Energy Market Problem, 13-th International symposium on dynamic games and applications, Wroclav, Poland, 2008.
Staňková, K. and Olsder, G.J. Properties and Analysis of Inverse Stackelberg Problems, Sixth International ISDG Workshop, Rabat, Morocco, 2007.
Staňková, K., Olsder, G.J. and Bliemer, M.C.J. Games of Stackelberg Type in Bilevel Toll Design Problem, Ninth Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics, HEC Montreal, Canada, 2007.
Staňková, K. Stackelberg Games & Their Application in Energy Markets, 22nd Conference on Operational Research, Prague, Czech Republic, 2007.
Staňková, K. On Freeway Traffic State Estimation/Prediction Using the Linear Switching Model. INRIA Grenoble, France, February 2010. (internal report)
Núñez, A., Picasso, B., De Vito, D., Scattolini, R., Colaneri, P., Espinosa, J., Valencia, F., De Schutter, B. and Staňková, K. Report on newly developed coordination mechanisms for hierarchical and distributed MPC. Deliverable D3.3.2, European FP7 STREP project HD-MPC, 49 pp., August 2010.
Staňková, K. and Abate, A. Study of a game-theoretical model describing interactions between predatory and prey mites, Delft Center for Systems and Control, Delft University of Technology, 40 pp., August 2011.
Some of the invited lectures
January 2012, Institute for Biodiversity and Ecosystem Dynamics, Amsterdam, The Netherlands, title: A game-theoretical study of the interactions between predatory mites and fruit-tree red spider mites.
November 2011, DCSMB Colloquium, Delft Center Of Microbial Systems Biology, Delft, The Netherlands, title: A game-theoretical study of the interactions between predatory mites and fruit-tree red spider mites.
September 2010, Viscosity Seminar, Centrum Wiskunde & Informatica, Amsterdam, The Netherlands, title: Differential games and their relation to viscosity solutions of the partial differential equations.
April 2007, Leibniz Institute Hannover, title: Stackelberg games: Properties and Applications, for slides and videostream see this link.
December 2008, Colloquium Control and System Theory, CWI Amsterdam, title: On inverse Stackelberg games & their application in optimal toll design problem
December 2008, Grenoble, Network controlled systems team seminar, title: Inverse Stackelberg games with applications to toll-based traffic control