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

rejecting Cournot-unstable equilibria. Indeed, even when one ignores the focal
nature derived from their symmetry, it is worthwhile to observe that these equi-
libria cannot be ruled out on account of any of the standard Nash equilibrium
refinements, such as normal-form perfection or strategic stability (Kohlberg and
Mertens, 1986).² Furthermore, in an experimental setting involving a symmet-
ric two-player game with one unstable symmetric equilibrium and a pair of
asymmetric equilibria, Cox and Walker (1998) found little support in the data
for any of the three equilibria. This provocative finding suggests that while a
Cournot-unstable equilibrium of a given game may be justifiably regarded as
unobservable, it does not thereby follow that some Cournot-stable equilibrium
of the same game will necessarily prevail and thus be observable. Rather, the
presence of both Cournot-stable and unstable equilibria may engender a high
level of indeterminacy, which may critically reduce the predictive power of the
game.

Our findings may also be advanced as a rebuttal to the aforementioned
criticism from the business strategy literature. Indeed, while sharing their mo-
tivation for understanding intra-industry heterogeneity, this approach underlies
a general methodology for generating inter-firm differences out of a strategic
game with fully rational and completely informed players. The contrast with
the evolutionary explanation is rather striking. Instead of discretionary differ-
ences that inevitably arise out of the idiosyncratic heuristic response that each
firm develops in isolation from other firms as a result of its multi-faceted op-
eration in an extremely complex environment, we uncover strategic differences
that arise out of a fully-fledged game-theoretic interaction amongst firms in a
simple and completely known environment. We will return to this contrast in
the specific context of an R&D game in a subsequent section.

The present paper may also be motivated in relation to various broad strands
of literature in industrial economics dealing in some way with strategic endoge-

² Indeed, they are typically strict Nash equilibria (in the sense that a unilateral deviation
will lead to a strict loss for the deviator), and thus would survive any of the well-known
refinements.

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