In this chapter we’ll study John F. Nash’s fundamental notion of “equilibrium” in game theory. Following Nash, we’ll use the Brouwer Fixed-Point Theorem to prove the result at the heart of his 1994 Nobel Prize in Economics: For every finite non-cooperative game, the mixed-strategy extension has a Nash Equilibrium. All will be explained; no prior experience with game theory will be assumed.
KeywordsNash Equilibrium Payoff Function Mixed Strategy Pure Strategy Expected Payoff
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