| Description |
1 online resource (x, 128 pages) |
| Series |
SpringerBriefs in Mathematics, 2191-8198 |
|
SpringerBriefs in mathematics, 2191-8198
|
| Contents |
880-01 Introduction -- General Presentation of Mean Field Control Problems -- Discussion of the Mean Field game -- Discussion of the Mean Field Type Control -- Approximation of Nash Games with a large number of players -- Linear Quadratic Models -- Stationary Problems- Different Populations -- Nash differential games with Mean Field effect |
|
880-01/(S Machine generated contents note: 1. Introduction -- 2. General Presentation of Mean Field Control Problems -- 2.1. Model and Assumptions -- 2.2. Definition of the Problems -- 3. Mean Field Games -- 3.1. HJB-FP Approach -- 3.2. Stochastic Maximum Principle -- 4. Mean Field Type Control Problems -- 4.1. HJB-FP Approach -- 4.2. Other Approaches -- 4.3. Stochastic Maximum Principle -- 4.4. Time Inconsistency Approach -- 5. Approximation of Nash Games with a Large Number of Players -- 5.1. Preliminaries -- 5.2. System of PDEs -- 5.3. Independent Trajectories -- 5.4. General Case -- 5.5. Nash Equilibrium Among Local Feedbacks -- 6. Linear Quadratic Models -- 6.1. Setting of the Model -- 6.2. Solution of the Mean Field Game Problem -- 6.3. Solution of the Mean Field Type Problem -- 6.4. Mean Variance Problem -- 6.5. Approximate N Player Differential Game -- 7. Stationary Problems -- 7.1. Preliminaries -- 7.2. Mean Field Game Set-Up -- 7.3. Additional Interpretations -- 7.4. Approximate N Player Nash Equilibrium -- 8. Different Populations -- 8.1. General Considerations -- 8.2. Multiclass Agents -- 8.3. Major Player -- 8.3.1. General Theory -- 8.3.2. Linear Quadratic Case -- 9. Nash Differential Games with Mean Field Effect -- 9.1. Description of the Problem -- 9.2. Mathematical Problem -- 9.3. Interpretation -- 9.4. Another Interpretation -- 9.5. Generalization -- 9.6. Approximate Nash Equilibrium for Large Communities -- 10. Analytic Techniques -- 10.1. General Set-Up -- 10.1.1. Assumptions -- 10.1.2. Weak Formulation -- 10.2. Priori Estimates for u -- 10.2.1. L[∞] Estimate for u -- 10.2.2. L2(W1,2)) Estimate for u -- 10.2.3. Cα Estimate for u -- 10.2.4. Lp(W2,P) Estimate for u -- 10.3. Priori Estimates for m -- 10.3.1. L2(W1,2) Estimate -- 10.3.2. L[∞](L[∞]) Estimates -- 10.3.3. Further Estimates -- 10.3.4. Statement of the Global A Priori Estimate Result -- 10.4. Existence Result |
| Summary |
Mean field games and Mean field type control introduce new problems in Control Theory. The terminology games may be confusing. In fact they are control problems, in the sense that one is interested in a single decision maker, whom we can call the representative agent. However, these problems are not standard, since both the evolution of the state and the objective functional is influenced but terms which are not directly related to the state or the control of the decision maker. They are however, indirectly related to him, in the sense that they model a very large community of agents similar to the representative agent. All the agents behave similarly and impact the representative agent. However, because of the large number an aggregation effect takes place. The interesting consequence is that the impact of the community can be modeled by a mean field term, but when this is done, the problem is reduced to a control problem |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed October 21, 2013) |
| Subject |
Mean field theory.
|
|
Control theory.
|
|
Game theory.
|
|
Game Theory
|
|
SCIENCE -- Energy.
|
|
SCIENCE -- Mechanics -- General.
|
|
SCIENCE -- Physics -- General.
|
|
Teoría de control
|
|
Juegos, Teoría de
|
|
Control theory
|
|
Game theory
|
|
Mean field theory
|
| Form |
Electronic book
|
| Author |
Frehse, J. (Jens), author.
|
|
Yam, Phillip (Sheung Chi Phillip), author.
|
| ISBN |
9781461485087 |
|
1461485088 |
|
146148507X |
|
9781461485070 |
|
