The existence of hybrid equilibria and weak hybrid equilibria for multi-leader-multi-follower games

This paper introduces a kind of hybrid equilibrium to multi-leader-multi-follower games.The existence of hybrid equilibria of the games is proven via set-valued analysis.Our hybrid equilibria can include both noncooperative equilibria and cooperative equilibria in references as special cases.In addition, a weak hybrid equilibrium is introduced both for normal form games and multi-leader-multifollower games with infinitely many players.The existence of weak hybrid equilibria is established for infinitely many players.The notion of the weak hybrid equilibrium is a generalization of weak α-core in cooperative games.These equilibrium conceptions and results are new in multi-leader-multi-follower games.