Prof. Margarida Carvalho (University of Montreal): "Correlated, Nash and Stackelberg for integer programming representable games" – Integer programming games (IPGs) are flexible models allowing to describe the interaction of rational players. From the practical point of view, they can suitably model the interactions of decision makers in economics, healthcare, and international agreements, to name few. From the theoretical perspective, IPGs motivate the generalization of mathematical programming tools from "single-player" optimization and the quest on reasonable game solution concepts.
In the first part, I revisit the background on IPGs, describe algorithmic methodologies to compute correlated and Nash equilibria, and present computational experiments. In the second part, we focus on Nash games played by Stackelberg leaders and demonstrate how a series of results in polyhedra theory allow to show that they are IPG-representable. Moreover, an innter approximation algorithm for the computation of equilibria will be presented.