Endogenous Heterogeneity in Strategic Models: Symmetry-breaking via Strategic Substitutes and Nonconcavities

provided by Research Papers in Economics

ENDOGENOUS HETEROGENEITY IN STRATEGIC MODELS :
SYMMETRY-BREAKING VIA STRATEGIC SUBSTITUTES

AND NONCONCAVITIES

Rabah Amir* Filomena GarciaJ Malgorzata Knauff+

February 2006

Abstract

This paper is an attempt to develop a unified approach to endoge-
nous heterogeneity by constructing general class of two-player symmetric
games that always possess only asymmetric pure-strategy Nash equilibria.
These classes of games are characterized in some abstract sense by two
general properties: payoff non-concavities and some form of strategic sub-
stitutability. We provide a detailed discussion of the relationship of this
work with Matsuyama’s symmetry breaking framework and with business
strategy literature. Our framework generalizes a number of models deal-
ing with two-stage games, with long term investment decisions in the first
stage and product market competition in the second stage. We present
the main examples that motivate this study to illustrate the generality of
our approach.

Keywords: inter-firm heterogeneity, submodular games, business strat-
egy, innovation strategies. JEL Classification: C72, C62, L11.

‘Department of Economics, University of Arizona, Tucson, AZ 85721 (USA).

^Technical University of Lisbon, Resercher at UECE, www.iseg.utl.pt/~uece. email: fgar-
[email protected]

^Université Catholique de Louvain - CORE, Voie du Roman Pays, 34,1348 Louvain-la-
Neuve (Belgium) and Warsaw School of Economics, Al Niepodleglosci 162, 20-554, Warsaw
(Poland).

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