Projections and functions of Nash equilibria

Levy, Y. J. (2016) Projections and functions of Nash equilibria. International Journal of Game Theory, 45(1-2), pp. 435-459. (doi: 10.1007/s00182-015-0517-3)

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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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Levy, Dr John
Authors: Levy, Y. J.
College/School:College of Social Sciences > Adam Smith Business School > Economics
Journal Name:International Journal of Game Theory
Publisher:Springer-Verlag Heidelberg
ISSN:0020-7276
ISSN (Online):1432-1270
Published Online:02 December 2015
Copyright Holders:Copyright © Springer-Verlag Berlin Heidelberg 2015
First Published:First published in International Journal of Game Theory 45(1-2):435-459
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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