Scientific update
Strategic interactions in multi-agent systems: Game-theoretic approach
ASA researchers apply the Hamilton-Jacobi-Bellman equation – the tool at the center of the theory of dynamic programming – to study dynamic games. In 2014 results on theoretical advances on so-called generalized mini-max solutions to non-zero-sum games of two large groups of agents interacting randomly with each other were published in [1] and [2]. The dynamical Nash equilibrium was introduced into the framework of closed-loop controls; the theoretical results help reveal new qualitative insights regarding the equilibrium trajectory in evolutionary games.
References
[1] Krasovskii NA, Kryazhimskiy AV, Tarasyev AM (2014). Hamilton-Jacobi equations in evolutionary games, Proceedings of the Institute of Mathematics and Mechanics UrB RAS, 20(3):114-131 [In Russian, English version to appear]
[2] Krasovskii NA, Tarasyev АМ (2014). Algorithms for construction of equilibrium trajectories in dynamic bi-matrix games, Proceedings of the International Conference Dedicated to the 90th Anniversary of N.N. Krasovskii, Ekaterinburg, Institute of Mathematics and Mechanics UrB RAS – Ural Federal University, 119-121 [In Russian]
Research program