- MATHEMATICAL SOCIAL SCIENCES Journal
- July 2021
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We reconsider the theory of Thompson aggregators proposed by Marinacci and Montrucchio (Marinacci
and Montrucchio, 2010). We prove the existence of a Least Fixed Point (LFP) solution to the Koopmans
equation. It is a recursive utility function. Our proof turns on demonstrating the Koopmans operator is a
Scott continuous function when its domain is an order bounded subset of a space of bounded functions
defined on the commodity space. Kleene"s Fixed Point Theorem yields the construction of the LFP
by an iterative procedure. We argue the LFP solution is the Koopmans equation"s principal solution.
It is constructed by an iterative procedure requiring less information (according to an information
ordering) than approximations for any other fixed point. Additional distinctions between the LFP
and GFP (Greatest Fixed Point) are presented. A general selection criterion for multiple solutions for
functional equations and recursive methods is proposed.
- iterative procedures; koopmans equation; koopmans operator; least fixed point theory; recursive utility; scott continuity; thompson aggregators