Projections and functions of Nash equilibria

Yehuda Levy

International Journal of Game Theory, 2016, vol. 45, issue 1, No 19, 435-459

Abstract: Abstract We show that any non-empty compact semi-algebraic subset of mixed action profiles on a fixed player set can be represented as the projection of the set of equilibria of a game in which additional binary players have been added. Even stronger, we show that any semi-algebraic continuous function, or even any semi-algebraic upper-semicontinuous correspondence with non-empty convex values, from a bounded semi-algebraic set to the unit cube can be represented as the projection of an equilibrium correspondence of a game with binary players in which payoffs depend on parameters from the domain of the function or correspondence in a multi-affine way. Some extensions are also presented.

Keywords: Nash equilibrium; Structure theorem; Semialgebraic geometry (search for similar items in EconPapers)
JEL-codes: C62 C65 C72 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00182-015-0517-3

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