Resolución numérica de juegos diferenciales deterministas y estocásticos en equilibrios de Nash

Resumen

The goal of this thesis is the design and implementation of a numerical algorithm for solving deterministic and stochastic infinite horizon differential games in closed-loop Nash equilibria. These games are specially relevant since, in the Literature, are the most commonly used due to their wide range of applications. We call the algorithm RaBVItG (Radial Basis and Value Iteration for Games) trying to specify the main characteristics of its design.The algorithm introduced here can be considered innovative because, as far as we know, we have not found a competitor solving both deterministic and stochastic cases. Additionally, the algorithm has a "mesh-free" design, so that it is possible to solve games with N players, where N is considerably greater than 2. We use the reference papers [13] in the deterministic case and [76] in the stochastic, as two main works to compare with our results.Our remarkable results are twofold. On the one hand, the algorithm’s efficiency: Comparing with [13], RaBVItG outperforms needing less computational time and lower errors. This is possible, in general, due to the advantages of the "mesh-free" computational design. On the other hand, we apply our algorithm to two problems borrowed from two scientific fields such as Marketing and Mathematical Psychology. Both contributions are opening future researching lines to use the algorithm and its future improvements...