Open AccessExistence and essential stability of Nash equilibria for biform games with Shapley allocation functions
Author(s) -
Chenwei Liu,
AUTHOR_ID,
Shuwen Xiang,
Yanlong Yang,
AUTHOR_ID
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022432
Subject(s) - nash equilibrium , mathematical economics , mathematics , best response , correlated equilibrium , extension (predicate logic) , epsilon equilibrium , function (biology) , stability (learning theory) , folk theorem , set (abstract data type) , combinatorics , mathematical optimization , game theory , normal form game , repeated game , equilibrium selection , computer science , evolutionary biology , machine learning , programming language , biology
We define the Shapley allocation function (SAF) based on the characteristic function on a set of strategy profiles composed of infinite strategies to establish an n -person biform game model. It is the extension of biform games with finite strategies and scalar strategies. We prove the existence of Nash equilibria for this biform game with SAF, provided that the characteristic function satisfies the linear and semicontinuous conditions. We investigate the essential stability of Nash equilibria for biform games when characteristic functions are perturbed. We identify a residual dense subclass of the biform games whose Nash equilibria are all essential and deduce the existence of essential components of the Nash equilibrium set by proving the connectivity of its minimal essential set.