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Equilibrium Existence and Uniqueness in Public Good Models: An Elementary Proof via Contraction
Author(s) -
Cornes Richard,
Hartley Roger,
Sandler Todd
Publication year - 1999
Publication title -
journal of public economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.809
H-Index - 32
eISSN - 1467-9779
pISSN - 1097-3923
DOI - 10.1111/1097-3923.00023
Subject(s) - uniqueness , mathematical economics , intuition , nash equilibrium , exploit , contraction (grammar) , elementary proof , economics , simple (philosophy) , general equilibrium theory , contraction mapping , mathematics , microeconomics , computer science , mathematical analysis , pure mathematics , fixed point , philosophy , medicine , computer security , epistemology
This paper presents a proof for existence and uniqueness of a Nash equilibrium of a public good model that exploits a simple contraction mapping. The proof establishes both existence and uniqueness in a single exercise that provides intuition about sufficiency. The method of proof is applied not only to the basic pure public good model but also to the impure model. In the latter model, income normality does not play the same pivotal role for existence and uniqueness.