Thompson aggregators, Scott continuous Koopmans operators, and Least Fixed Point theory Articles uri icon

publication date

  • July 2021

start page

  • 84

end page

  • 97


  • 112

International Standard Serial Number (ISSN)

  • 0165-4896

Electronic International Standard Serial Number (EISSN)

  • 1879-3118


  • 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.


  • Economics


  • iterative procedures; koopmans equation; koopmans operator; least fixed point theory; recursive utility; scott continuity; thompson aggregators