scholarly journals Open and Closed Loop Nash Equilibria in Games with a Continuum of Players

2013 ◽  
Vol 160 (1) ◽  
pp. 280-301 ◽  
Author(s):  
Agnieszka Wiszniewska-Matyszkiel
Keyword(s):  
Nash Equilibria ◽  
Closed Loop ◽  
Continuum Of Players

scholarly journals Two-Player Location Game in a Closed-Loop Market with Quantity Competition

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Xiaofeng Chen ◽  
Qiankun Song ◽  
Zhenjiang Zhao
Keyword(s):  
Minimum Distance ◽  
Nash Equilibria ◽  
Closed Loop ◽  
Transportation Cost ◽  
Competitive Dynamics ◽  
Backward Induction ◽  
Local Market ◽  
Induction Method ◽  
Quantity Competition ◽  
Circle Model

This paper considers the two-player location game in a closed-loop market with quantity competition. Based on the Cournot and Hotelling models, a circle model is established for a closed-loop market in which two players (firms) play a location game under quantity competition. Using a two-stage (location-then-quantity) pattern and backward induction method, the existence of subgame-perfect Nash equilibria is proved for the location game in the circle model with a minimum distance transportation cost function. In addition, sales strategies are proposed for the two players for every local market on the circle when the players are in the equilibrium positions. Finally, an algorithm for simulating the competitive dynamics of the closed-loop market is designed, and two numerical simulations are provided to substantiate the effectiveness of the obtained results.

scholarly journals Uncoupling Isaacs’equations in nonzero-sum two-player differential games : The example of conflict over parental care

2008 ◽  
Vol Volume 9, 2007 Conference in... ◽  
Author(s):  
Frédéric Hamelin ◽  
Pierre Bernhard
Keyword(s):  
Parental Care ◽  
Differential Games ◽  
Nash Equilibria ◽  
Closed Loop ◽  
Classical Problem ◽  
Complete Analysis ◽  
Behavioural Ecology ◽  
International Audience ◽  
Set Up

International audience We use a recently uncovered decoupling of Isaacs PDE’s of some mixed closed loop Nash equilibria to give a rather complete analysis of the classical problem of conflict over parental care in behavioural ecology, for a more general set up than had been considered heretofore. On utilise un découplage récemment mis en évidence des équations d’Isaacs d’un jeu différentiel pour des stratégies mixtes singulières particulières pour donner une analyse assez complète d’un problème classique en écologie comportementale concernant le conflit à propos des soins parentaux.

scholarly journals Approximation and characterization of Nash equilibria of large games

2020 ◽  
Author(s):  
Guilherme Carmona ◽  
Konrad Podczeck
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Large Games ◽  
Finite Games ◽  
Continuum Of Players ◽  
The Relationship

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.

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