Existence of robust weak Nash equilibria for leader-follower games with uncertainty

This paper mainly proposes the notion of robust weak Nash equilibria for multi-objective leader-follower games with uncertainty and proves their existence. Firstly, based on l-type set relations, robust weak Nash equilibria for n-person noncooperative games are introduced and their existence are proved by Fan-Glicksberg’s fixed point theorem. Secondly, such robust weak Nash equilibria are further put forward for multi-objective single-leader-multi-follower games with uncertainty, and their existence are furthermore shown. Two examples illustrate the validity of the existence results respectively. Our results are novel from the current ones.