Extended Nash Equilibria of Nonmonetized Noncooperative Games on Preordered Sets

A noncooperative game is said to be nonmonetized if the ranges of the utilities (payoffs) of the players are preordered sets. In this paper, we examine some nonmonetized noncooperative games in which both of the collection of strategies and the ranges of the utilities for the players are preordered sets. Then, we spread the concept of extended Nash equilibria of noncooperative games from posets to preordered sets. By applying some fixed point theorems on preordered sets and by using the order preserving property of the utilities, we prove an existence theorem of extended Nash equilibria for nonmonetized noncooperative games.