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Measures of economies with an arbitrarily large number of equilibria
Author(s) -
Loi Andrea,
Matta Stefano
Publication year - 2012
Publication title -
international journal of economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.351
H-Index - 11
eISSN - 1742-7363
pISSN - 1742-7355
DOI - 10.1111/j.1742-7363.2012.00194.x
Subject(s) - measure (data warehouse) , infinity , economics , zero (linguistics) , economy , space (punctuation) , set (abstract data type) , mathematical economics , mathematics , computer science , mathematical analysis , linguistics , philosophy , database , programming language , operating system
Balasko (1978) shows that in a compact subset of the space of economies, not too many economies can have too many equilibria. We extend Balasko’s result to the whole set of economies for a suitable measure. We show that the measure of economies with a large number of equilibria approaches zero as this number tends to infinity. An analogous result in the infinite‐dimensional setting is also established.