Finding Nash equilibria in noncooperative games

Author(s):  
Antoon van den Elzen
2015 ◽  
Vol 17 (01) ◽  
pp. 1540009
Author(s):  
Jinlu Li

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.


1991 ◽  
Vol 7 (1) ◽  
pp. 37-65 ◽  
Author(s):  
Giacomo Bonanno

For the past 20 years or so the literature on noncooperative games has been centered on the search for an equilibrium concept that expresses the notion of rational behavior in interactive situations. A basic tenet in this literature is that if a “rational solution” exists, it must be a Nash equilibrium. The consensus view, however, is that not all Nash equilibria can be accepted as rational solutions. Consider, for example, the game of Figure 1.


Erkenntnis ◽  
2021 ◽  
Author(s):  
Chiara Lisciandra

AbstractIn this paper, I outline and defend the view that variations in compliance levels with one and the same norm represent different norms about following norms. In support of this claim, I first argue that classic game-theoretic accounts, which define norms as Nash equilibria of noncooperative games, typically consider variations in compliance levels as separate norms. After that, I suggest a more fine-grained, game-theoretic distinction that accounts for degrees of compliance with the same norm and I show how to incorporate such an account into a psychological framework. Finally, the paper examines what given degrees of compliance can reveal about the dynamics underlying the process of norm change. I will argue that they are indicators of different reactions to the introduction of new norms.


2021 ◽  
Vol 4 (2) ◽  
pp. 178-199
Author(s):  
Vadim Romanuke ◽  

A theory of refining pure strategy efficient Nash equilibria in finite noncooperative games under uncertainty is outlined. The theory is based on guaranteeing the corresponding payoffs for the players by using maximultimin, which is an expanded version of maximin. If a product of the players’ maximultimin subsets contains more than one efficient Nash equilibrium, a superoptimality rule is attached wherein minimization is substituted with summation. The superoptimality rule stands like a backup plan, and it is involved if maximultimin fails to produce just a single refined efficient equilibrium (a metaequilibrium). The number of the refinement possible outcomes is 10. There are 3 single-metaequilibrium cases, 3 partial reduction cases, and 4 fail cases. Despite successfulness of refinement drops as the game gets bigger, pessimistic estimation of its part is above 54 % for games with no more than four players.


Sign in / Sign up

Export Citation Format

Share Document