Applications of fixed point theory to extended Nash equilibriums of nonmonetized noncooperative games on posets

摘要

We say that a noncooperative game is nonmonetized if the ranges of the utilities of the players are posets. In this paper, we examine some nonmonetized noncooperative games of which both the collection of strategies and the ranges of the utilities for the players are posets. Then we carry the concept of generalized Nash equilibriums of noncooperative games defined in (Li in J. Nonlinear Anal. Forum 18:1-11, 2013; Li and Park in Br. J. Econ. Manag. Trade 4(1), 2014) to extended Nash equilibriums of nonmonetized noncooperative games. By applying some fixed point theorems in posets and by using the order-preserving property of mappings, we prove an existence theorem of extended Nash equilibriums for nonmonetized noncooperative games. MSC:46B42, 47H10, 58J20, 91A06, 91A10.