Theoretical Economics, Volume 12, Number 2 (May 2017)

Theoretical Economics 12 (2017), 533–554

On the equivalence of large individualized and distributionalized games

Mohammed Ali Khan, Kali P. Rath, Haomiao Yu, Yongchao Zhang


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

Full Text:  PRINT  VIEW