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The following slides contain both well-known results in the literature and also unpublished results of the author. Typos and mistakes are to be expected and readers should use it with discretion. Corrections and feedbacks are much appreciated. If you are planning to use any of the materials in these slides, proper citation is to be expected and appreciated. Regular updates on these slides are also expected and please come back and check for the latest update at your convenience.
Teaching Materials (slides)
Lattice: algebraic structure of sublattice and Birkhoff's representation theorem
Submodular function and increasing differences: preserving operations on domain and co-domain
Quasi-supermodular and single crossing: characterization of the monotone optimal solutions
Lovasz extension: Choquet perspective for finite and infinite games
Owen (multilinear) extension and Lyapunov function approach for approximation design and analysis
Parametric optimization: monotone comparative statics
Cooperative games: submodular games and core
Non-cooperative games: Tarski's and Zhou’s lattice fixed-point theorem and their applications to existence of Nash equilibrium
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