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Game Theory and Learning for Wireless Networks by Hamidou Tembine, Samson Lasaulce

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Chapter 2. Playing with Equilibria in Wireless Non-Cooperative Games
Nash equilibria can be the solutions of different classes of non-cooperative games involving rational players, or they can be the result of a learning process.
Nash equilibria can be pure or mixed, and, mathematically speaking, proving the existence of a Nash equilibrium amounts to proving the existence of a solution to a fixed-term problem. Some useful existence theorems and their applications are introduced.
If a Nash equilibrium can be proved to exist, the next step is to find out if it is unique; this is desirable if the performance of a system or outcome of a dynamic process is to be predicted. Uniqueness can only be proven under certain conditions.
Nash equilibria are typically ...

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