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Published online by Cambridge University Press: 05 May 2022
In this chapter, we proveKakutani's Fixed Point Theorem, which is an extension of Brouwer's Fixed Point Theoremto correspondences (set-valued mappings). We then define the concept of $\lambda$-discounted equilibrium, and using Kakutani's Fixed Point Theorem we prove that every multiplayer stochastic game admits a stationary $\lambda$-discounted equilibrium, for every discount factor $\lambda \in (0,1]$.
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