Existence and stability of Nash equilibrium

• Main Author: Carmona, Guilherme.
• Corporate Author: World Scientific (Firm)
• Format: Electronic
• Language: English
• Published: Singapore ; Hackensack, N.J. : World Scientific Pub. Co., c2013.
• Subjects: Game theory.; Equilibrium (Economics); Electronic books.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://www.worldscientific.com/worldscibooks/10.1142/8406#t=toc

The book aims at describing the recent developments in the existence and stability of Nash equilibrium. The two topics are central to game theory and economics and have been extensively researched. Recent results on existence and stability of Nash equilibrium are scattered and the relationship betwe...

Table of Contents:

• 1. Introduction
• 2. Continuous normal-form games. 2.1. Notation and definitions. 2.2. Existence of Nash equilibria. 2.3. Mixed strategies. 2.4. Stability of Nash equilibria. 2.5. Existence of Nash equilibria via approximate equilibria. 3. Generalized better-reply secure games. 3.1. Generalized better-reply security and existence of equilibrium. 3.2. Examples. 3.3. Two characterizations of generalized better-reply security. 3.4. Better-reply security. 3.5. Sufficient conditions. 3.6. Mixed strategies. 3.7. References
• 4. Stronger existence results. 4.1. Multi-player well-behaved security. 4.2. Diagonal transfer continuity. 4.3. Generalized C-security. 4.4. Lower single-deviation property. 4.5. Generalized weak transfer continuity. 4.6. References
• 5. Limit results. 5.1. A general limit result. 5.2. Two characterization of the limit problem for æ-equilibria. 5.3. Sufficient conditions for limit results. 5.4. Existence of æ-equilibrium. 5.5. Continuity of the Nash equilibrium correspondence. 5.6. Strategic approximation. 5.7. References
• 6. Games With an endogenous sharing rule. 6.1. Existence and stability of solutions. 6.2. References
• 7. Games With a continuum of players. 7.1. Notation and definitions. 7.2. Existence of equilibrium distributions. 7.3. Relationship With finite-player games. 7.4. Proof of the existence theorem for non-atomic games. 7.5. References.