Goals, motivation
Game theory is concerned generally with the analysis of conflict and cooperation. Used commonly in Economics, it is progressively making its way in Engineering sciences. Among the many game-theoretical models, stochastic dynamic games ideally represent situations where agents interact in time in an environment fraught with uncertainty. However, the practical impact of the theory is limited by several concerns, some of which will be at the center of this project:
- Lack of “solution” to the game (equilibria), or lack of uniqueness of it, which deprive models of any prediction value
- Proper modeling of the rationality of agents and the information they gather or use
- Lack of efficient algorithms to calculate solutions.
This project brings together researchers from Applied Mathematics, Operations Research and Economics with the global objective to propose advances in the theory and practice of dynamic stochastic games.
Methodology
We shall follow the work program quite usual in Applied Mathematics. Starting with problems of more practical nature, we shall propose mathematical models taking into account the salient features. When “solving” these models, we shall seek at the same time: to identify generic features and corresponding high-level properties that will apply to similar models, and: exploit the specific structure of the model for more efficient algorithms. Results obtained should include theoretical results (existence, uniqueness, approximability, …), algorithms and their analysis (complexity, convergence rate, …) and tests on practical situations originating from, e.g., law enforcement problems (cops and robber games, network games) or the sustainability of natural resources (bio-economic models, etc.).
