Theoretical Economics 12 (2017), 533–554

The theory of large one-shot simultaneous-play games with a bio-social typology has been presented in both the individualized and distributionalized forms, LIG and LDG respectively. Using an example of an LDG with two actions and a single trait in which some Nash equilibrium distributions cannot be induced by the Nash equilibria of the representing LIG, this paper offers three equivalence results that delineate a relationship between the two game-forms. Our analysis also reveals the different roles that the Lebesgue unit interval and a saturated space play in the theory.

Keywords: Distributionalized games, individualized games, Nash equilibrium distribution, Nash equilibrium, representation, equivalence, weak-equivalence, quasi-equivalence, realization, similarity, symmetry, countability, saturation

JEL classification: C62, D50, D82, G13