A unified approach to the Nash equilibrium existence in large games from finitely many players to infinitely many players

Author(s):  
Zhe Yang ◽  
Qingping Song
2020 ◽  
Author(s):  
Guilherme Carmona ◽  
Konrad Podczeck

Abstract We characterize Nash equilibria of games with a continuum of players in terms of approximate equilibria of large finite games. This characterization precisely describes the relationship between the equilibrium sets of the two classes of games. In particular, it yields several approximation results for Nash equilibria of games with a continuum of players, which roughly state that all finite-player games that are sufficiently close to a given game with a continuum of players have approximate equilibria that are close to a given Nash equilibrium of the non-atomic game.


2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Zahra Al-Rumaih ◽  
Souhail Chebbi ◽  
Hong Kun Xu

We prove an equilibrium existence result for vector functions defined on noncompact domain and we give some applications in optimization and Nash equilibrium in noncooperative game.


Game Theory ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Dionysius Glycopantis

This paper adds to the discussion, in a general setting, that given a Nash-Schmeidler (nonanonymous) game it is not always possible to define a Mas-Colell (anonymous) game. In the two games, the players have different strategic behaviours and the formulations of the two problems are different. Also, we offer a novel explanation for the lack of a Nash equilibrium in an infinite game. We consider this game as the limit of a sequence of approximate, finite games for which an equilibrium exists. However, the limiting pure strategy function is not measurable.


2021 ◽  
Vol 13 (2) ◽  
pp. 62-79
Author(s):  
Юлия Васильевна Чиркова ◽  
Julia Chirkova

The Machine Load Balancing Game with linear externalities is considered. A set of jobs is to be assigned to a set of machines with different latencies depending on their own loads and also loads on other machines. Jobs choose machines to minimize their own latencies. The social cost of a schedule is the maximum delay among all machines, i.e. {\it makespan. For the case of two machines in this model an Nash equilibrium existence is proven and of the expression for the Price of Anarchy is obtained.


2016 ◽  
pp. 116-128
Author(s):  
O.P. Ignatenko ◽  

This paper deals with modeling of network’s dynamic using game theory approach. The process of interaction among players (network users), trying to maximize their payoffs (e.g. throughput) could be analyzed using game-based concepts (Nash equilibrium, Pareto efficiency, evolution stability etc.). In this work we presented the model of TCP network’s dynamic and proved existence and uniqueness of solution, formulated payoff matrix for a network game and found conditions of equilibrium existence depending of loss sensitivity parameter. We consider influence if denial of service attacks on the equilibrium characteristics and illustrate results by simulations.


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