Arrow-Debreu framework is established and equilibrium notion is introduced. Existence properties are discussed and formally proved. Stability of the equilibria is discussed and the conditions are introduced. Uniqueness is discussed next. In game theory, we start by introducing the basic set-up of a complete information simultaneous move game. The concept of Nash equilibrium is formally discussed. The existence of Nash equilibrium is proved and the related conditions are introduced. The assumption of complete information is relaxed next and Bayes Nash equilibrium is introduced. The sequential game concept if defined next and the appropriate notion of equilibrium is discussed. Several examples from market structures, auctions, voting etc. are used to motivate the notions and explain the concepts.
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