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



explain ”the diversity across space, time and groups” (Matsuyama, 2002).

In view of the diversity of economic research areas involved in this effort, it
is not surprising that various conceptual and methodological approaches have
been developed in connection with this complex task. While often tailored to
a specific area, each of these approaches is broad in explanatory scope and
has wide potential applicability. We now briefly review three of these general
paradigms that share some relationship to the present paper.

The dominant approach, based on coordination failures, postulates a game
with strategic complementarities and multiple Pareto-ranked pure-strategy Nash
equilibrium points. Diversity is then synonymous with making different equilib-
rium selections, with the high-performing entity picking the Pareto-dominant
equilibrium and the low-performing entity failing to do so. This argument is
thus generally predicated on the presence of two identical and non-interacting
economies, each operating under a different equilibrium out of the same equi-
librium set. It may also be invoked to explain diversity across time within the
same economy, with booms and recessions corresponding to operation under the
Pareto dominant and inferior equilibria respectively. This literature includes as
key studies Cooper and John (1988), Murphy, Schleifer and Vishny (1989), and
is surveyed by Cooper (1999).

The coordination failures approach has been criticized for failing to offer
any compelling argument for the diversity in equilibrium selections in the two-
economy model or for the regime switch in the one-economy model. Matsuyama
(2002) proposes a modification of the former model by creating an interac-
tive link between the two sub-economies and allowing the two players to take
two decisions, one in each sub-economy. Under some conditions on the larger
game with a priori identical players, namely that the players’ actions are pair-
wise strategic complements and each player’s actions are substitutes due to a
fixed total resource constraint, multiple equilibria arise with the property that
the symmetric equilibrium is unstable while the two asymmetric equilibria are
stable, both in the sense of Cournot dynamics. Endogenous heterogeneity in
this approach is then predicated on the central postulate that only Cournot-



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