Open AccessOn the equivalence of large individualized and distributionalized games
Author(s) -
Khan Mohammed Ali,
Rath Kali P.,
Yu Haomiao,
Zhang Yongchao
Publication year - 2017
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te1806
Subject(s) - equivalence (formal languages) , mathematical economics , biosocial theory , nash equilibrium , mathematics , game theory , space (punctuation) , best response , pure mathematics , computer science , social psychology , psychology , personality , operating system
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.