On the equivalence of large individualized and distributionalized games - Mohammed Ali Khan; Kali P. Rath; Haomiao Yu; Yongchao Zhang (Theoretical Economics, 2017)
The theory of large one-shot simultaneous-play games with a biosocial typology has been presented in both the individualized and distributionalized forms-large individualized games (LIG) and large distributionalized games (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: C62; D50; D82; G13; 330; Distributionalized games; individualized games; Nash equilibrium distribution; Nash equilibrium; representation; equivalence; weak equivalence; quasi-equivalence; realization; similarity; symmetry; countability; saturation