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Two Stage 2x2 Games with Strategic Substitutes and Strategic Heterogeneity

Feng and Sabarwal (2018) show that there is additional scope to study strategic complements in extensive form games, by investigating in detail the case of two stage, 2×2 games. We show the same for two stage, 2 × 2 games with strategic substitutes and with strategic heterogeneity. We characterize strategic substitutes and strategic heterogeneity in such games, and show that the set of each class of games has infinite Lebesgue measure. Our conditions are easy to apply and yield uncountably many examples of such games, indicating greater possibilities for the manifestation and study of these types of interactions. In contrast to the case for strategic complements, we show that generically, the set of subgame perfect Nash equilibria in both classes of games is totally unordered (no two equilibria are comparable). Consequently, with multiple equilibria, some nice features of strategic complements that depend on the complete lattice structure of the equilibrium set may not transfer to the case of strategic substitutes or strategic heterogeneity.