Competing Pre-match Investments Revisited: A Characterization of Monotone Bayes-Nash Equilibria in Large Markets

2020 ◽  
Author(s):  
Deniz Dizdar
Keyword(s):  
Nash Equilibria

Competitive Framing

2014 ◽  
Vol 6 (3) ◽  
pp. 35-58 ◽  
Author(s):  
Ran Spiegler
Keyword(s):  
Industrial Organization ◽  
Consumer Choice ◽  
Nash Equilibria ◽  
Market Competition ◽  
Behavioral Industrial Organization ◽  
Marketing Messages

I present a simple framework for modeling two-firm market competition when consumer choice is “frame-dependent,” and firms use costless “marketing messages” to influence the consumer’s frame. This framework embeds several recent models in the “behavioral industrial organization” literature. I identify a property that consumer choice may satisfy, which extends the concept of Weighted Regularity due to Piccione and Spiegler (2012), and provide a characterization of Nash equilibria under this property. I use this result to analyze the equilibrium interplay between competition and framing in a variety of applications. (JEL D43, D82, M31)

scholarly journals Stochastic differential games with inside information

2016 ◽  
Vol 19 (03) ◽  
pp. 1650016 ◽  
Author(s):  
Olfa Draouil ◽  
Bernt Øksendal
Keyword(s):  
White Noise ◽  
Differential Games ◽  
Malliavin Calculus ◽  
Model Uncertainty ◽  
Nash Equilibria ◽  
Stochastic Calculus ◽  
Stochastic Differential Games ◽  
Inside Information ◽  
Jump Diffusions

We study stochastic differential games of jump diffusions, where the players have access to inside information. Our approach is based on anticipative stochastic calculus, white noise, Hida–Malliavin calculus, forward integrals and the Donsker delta functional. We obtain a characterization of Nash equilibria of such games in terms of the corresponding Hamiltonians. This is used to study applications to insider games in finance, specifically optimal insider consumption and optimal insider portfolio under model uncertainty.

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.

scholarly journals On Perfect Nash Equilibria of Polymatrix Games

Game Theory ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Slim Belhaiza
Keyword(s):  
Nash Equilibria ◽  
Convex Polytopes ◽  
Finite Union ◽  
Perfect Equilibrium ◽  
Small Game ◽  
Dominated Strategies ◽  
Polymatrix Games ◽  
Linear Programming Formulation ◽  
Perfect Equilibria

When confronted with multiple Nash equilibria, decision makers have to refine their choices. Among all known Nash equilibrium refinements, the perfectness concept is probably the most famous one. It is known that weakly dominated strategies of two-player games cannot be part of a perfect equilibrium. In general, this undominance property however does not extend to n-player games (E. E. C. van Damme, 1983). In this paper we show that polymatrix games, which form a particular class of n-player games, verify the undominance property. Consequently, we prove that every perfect equilibrium of a polymatrix game is undominated and that every undominated equilibrium of a polymatrix game is perfect. This result is used to set a new characterization of perfect Nash equilibria for polymatrix games. We also prove that the set of perfect Nash equilibria of a polymatrix game is a finite union of convex polytopes. In addition, we introduce a linear programming formulation to identify perfect equilibria for polymatrix games. These results are illustrated on two small game applications. Computational experiments on randomly generated polymatrix games with different size and density are provided.

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