Interval methods for computing strong Nash equilibria of continuous games

Abstract

The problem of seeking strong Nash equilibria of a continuous game is considered. For some games, these points cannot be found analytically, only numerically. Interval methods provide us with an approach to rigorously verify the existence of equilibria in certain points. A proper algorithm is presented. We formulate and prove propositions, that give us features which have to be used by the algorithm (to the best knowledge of the authors, these propositions and properties are original). Parallelization of the algorithm is also considered, and numerical results are presented. As a particular example, we consider the game of »misanthropic individuals«, a game, invented by the first author, that may have several strong Nash equilibria depending on the number of players. Our algorithm is able to localize and verify these equilibria.