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Analysis of migration dynamics using PDE approach to games

Maksim Mazuryn: How can a fish win in a game with infinitely many players?

Classical game theory provides tools to analyse situations where players have conflicting interests, i.e. each player has a distinct payoff function and it depends on the decisions of all the players.  Usually a strategy which results in the best outcome for everyone doesn’t exist and one can introduce various notions of an optimal profile of strategies, for example the Nash equilibrium, to capture different aspects of interest in the game. Another feature of classical game theory is that a player can affect the resulting gains for all the players by playing a different strategy.

But what if the number of agents in a game is very large? Then analysis of the game is simplified by the fact that each player has insignificant influence on the overall evolution of the system. Such a game is called a mean field game and a theory of mean field games emerged from models in economics and finance.

The PhD project deals with diel vertical migration -- one of the largest daily movements of marine species where animals remain in deep, dark water in daylight hours to avoid visual predation and migrate to upper levels at dusk to feed. The migration of each organism can be rationalized as a trade-off between growth and survival with strategies as spatial distributions of populations. The idea of this project is to consider the diel vertical migration as a game each organism is playing against the others to maximize its biological fitness. Since the game involves large population of players, the aim is to develop mean field game framework to analyse and explain the migration process in terms of optimal strategies.

PhD project

By: Maksim Mazuryn

Section: Dynamical Systems

Principal supervisor: Uffe Høgsbro Thygesen

Co-supervisors: Mirza Karamehmedovic, Andre Visser

Project title: Analysis of migration dynamics using PDE approach to games

Term: 01/07/2019 → 30/09/2022

Contact

Uffe Høgsbro Thygesen
Associate Professor
DTU Compute
+45 45 25 30 60

Contact

Mirza Karamehmedovic
Associate Professor
DTU Compute
+45 45 25 30 20

Contact

Andre Visser
Professor
DTU Aqua
+45 35 88 34 25