Inverse maximum theorems and some consequences

John Cotrina, Raúl Fierro

Research output: Working paper


We deal with inverse maximum theorems, which are inspired by the ones given by Aoyama, Komiya, Li et al., Park and Komiya, and Yamauchi. As a consequence of our results, we state and prove an inverse maximum Nash theorem and show that any generalized Nash game can be reduced to a classical Nash game, under suitable assumptions. Additionally, we show that a result by Arrow and Debreu, on the existence of solutions for generalized Nash games, is actually equivalent to the one given by Debreu-Fan-Glicksberg for classical Nash games, which in turn is equivalent to Kakutani-Fan-Glisckberg's fixed point theorem.
Original languageEnglish
PublisherCornell University
Number of pages17
StatePublished - 9 Aug 2022


  • Inverse maximum theorem
  • Berge's maximum theorem
  • Generalized Nash game
  • Kakutani’s fixed point theorem


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