Abstract
This paper develops two different generalized classes of supermodular functions and games. The first class called Lambda supermodular functions are stronger than Pseudo-supermodular functions but is weaker than quasi-supermodular functions. The second class called Quasi-pseudosupermodular functions are weaker than the Pseudo-supermodular functions. We prove the corresponding Monotonicity theorem for the optimization involving such functions. As an application, we give generalizations of supermodular games and study the problem of the existence of undominated pure strategy Nash equilibria in this generalized games. We also characterize the general class of functions introduced in this paper in addition to the characterization of Pseudo-supermodular functions.
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