The Explicit form of Berge Strong Guaranteed Equilibrium in Linear-Quadratic Non-Cooperative Game

摘要

Previously, the authors introduced the concept of a Berge strong guaranteed equilibrium for non-cooperative games under uncertainty in the normal form and proved the existence in mixed strategies under some „habitual" constraints: the set of strategies of players and uncertainties is a compact one, and the payoff function is continuous. However, in previous studies, there have not been investigated classes of games with a rather general form, so that the mentioned solution would be found. The current paper is intended to eliminate this gap. Here we construct an explicit form of the Berge strong guaranteed equilibrium for a sufficiently broad class of linear-quadratic games under uncertainty. It includes, in particular, mathematical models of a competitive economy by Antoine Augustin Cournot and duopoly model of Joseph Bertrand.