Applications of fixed point theory to extended Nash equilibriums of nonmonetized noncooperative games on posets. (English) Zbl 1306.91009
Summary: 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 [J. Li, Nonlinear Anal. Forum 18, 1–11 (2013; Zbl 1293.91012); J. Li and S. Park, “Generalized Nash equilibria of nonmonetized noncooperative games on lattices”, Br. J. Econ. Manag. Trade 4, No. 1, 97–110 (2014; doi:10.9734/BJEMT/2014/4618)] 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:
| 91A10 | Noncooperative games |
| 91A06 | \(n\)-person games, \(n>2\) |
| 06A99 | Ordered sets |
| 46B42 | Banach lattices |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 47H10 | Fixed-point theorems |
| 58J20 | Index theory and related fixed-point theorems on manifolds |
Keywords:
poset; lattice; order-preserving mapping; fixed point; nonmonetized noncooperative game; generalized Nash equilibrium; extended Nash equilibriumCitations:
Zbl 1293.91012References:
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