Supermodular games

If quasi-concavity of the players payoffs cannot be verified, there is an alternative existence proof that relies on Tarski s (1955) fixed point theorem and involves the notion of supermodular games. The theory of supermodular games is a relatively recent development introduced and advanced by Topkis (1998). 

Theorem 3. In a supermodular game there exists at least one NE. 

Supermodular games approach. In some situations, supermodular games provide a more convenient tool for comparative statics. 

Theorem 11. Consider a collection of supermodular games on RP parameterized by a parameter a. Further, suppose d Kijdxida > 0 for all i. Then the largest and the smallest equilibria are increasing in a. 

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