Abstract
This paper constructs a one-leader-follower game with fuzzy mapping (OLFFG), and studies the existence of equilibrium point of OLFFG. First, we introduce the definition of fuzzy equilibrium point and slightly altruistic fuzzy equilibrium point of OLFFG. Furthermore, we prove that the existence of fuzzy equilibrium point and slightly altruistic fuzzy equilibrium point of OLFFG by the nonlinear analysis theory. Finally, it is proved that if the essential equilibrium point of OLFFG exists, it must be the slightly altruistic fuzzy equilibrium point.
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