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An application of Kleene's fixed point theorem to dynamic programming
Author(s) -
Kamihigashi Takashi,
Reffett Kevin,
Yao Masayuki
Publication year - 2015
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/ijet.12074
Subject(s) - fixed point , bellman equation , value (mathematics) , fixed point theorem , mathematics , least fixed point , dynamic programming , set (abstract data type) , operator (biology) , function (biology) , mathematical economics , point (geometry) , mathematical optimization , discrete mathematics , computer science , brouwer fixed point theorem , schauder fixed point theorem , mathematical analysis , statistics , repressor , chemistry , biology , biochemistry , geometry , evolutionary biology , transcription factor , programming language , gene
We show that the least fixed point of the Bellman operator in a certain set can be computed by value iteration whether or not the fixed point is the value function. As an application, we give a simpler proof of one of Kamihigashi's main results.