Ky Fan inequality (game theory)

In mathematics, there are different results that share the common name of the Ky Fan inequality. The Ky Fan inequality presented here is used in game theory to investigate the existence of an equilibrium. Another Ky Fan inequality is an inequality involving the geometric mean and arithmetic mean of two sets of real numbers of the unit interval.

Statement

Suppose that is a convex compact subset of a Hilbert space and that is a function from to satisfying

  • is lower semicontinuous for every and
  • is concave for every .

Then there exists such that

References

  • Aubin, Jean-Pierre. "Optima and Equilibria". Graduate Texts in Mathematics. 140. Springer-Verlag. doi:10.1007/978-3-662-03539-9. Cite journal requires |journal= (help)
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