TY - UNPB

T1 - Inverse maximum theorems and some consequences

AU - Cotrina, John

AU - Fierro, Raúl

PY - 2022/8/9

Y1 - 2022/8/9

N2 - 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.

AB - 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.

KW - Inverse maximum theorem

KW - Berge's maximum theorem

KW - Generalized Nash game

KW - Kakutani’s fixed point theorem

U2 - 10.48550/arXiv.2201.13136

DO - 10.48550/arXiv.2201.13136

M3 - Working paper

BT - Inverse maximum theorems and some consequences

PB - Cornell University

ER -