Nash Equilibrium

Fixed points in game theory
  • Joel H. Shapiro
Part of the Universitext book series (UTX)


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.


Nash Equilibrium Payoff Function Mixed Strategy Pure Strategy Expected Payoff 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Joel H. Shapiro
    • 1
  1. 1.Portland State UniversityPortlandUSA

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