Book contents
- Frontmatter
- Contents
- Preface
- 1 Overviews
- 2 Setting Up Dynamic Models
- 3 The Master Equation
- 4 Introductory Simple and Simplified Models
- 5 Aggregate Dynamics and Fluctuations of Simple Models
- 6 Evaluating Alternatives
- 7 Solving Nonstationary Master Equations
- 8 Growth and Fluctuations
- 9 A New Look at the Diamond Search Model
- 10 Interaction Patterns and Cluster Size Distributions
- 11 Share Market with Two Dominant Groups of Traders
- Appendix
- References
- Index
2 - Setting Up Dynamic Models
Published online by Cambridge University Press: 15 October 2009
- Frontmatter
- Contents
- Preface
- 1 Overviews
- 2 Setting Up Dynamic Models
- 3 The Master Equation
- 4 Introductory Simple and Simplified Models
- 5 Aggregate Dynamics and Fluctuations of Simple Models
- 6 Evaluating Alternatives
- 7 Solving Nonstationary Master Equations
- 8 Growth and Fluctuations
- 9 A New Look at the Diamond Search Model
- 10 Interaction Patterns and Cluster Size Distributions
- 11 Share Market with Two Dominant Groups of Traders
- Appendix
- References
- Index
Summary
This book is about setting up and analyzing economic models for large collections of interacting agents. We describe models in terms of states: as stationary distribution of states, or dynamics for time evolution of states. We may speak informally also of patterns of partitions of the set of agents by types or categories, or configurations, and how they or some functions of them evolve with time. Our models are usually specified as jump Markov processes, that is, Markov processes with a finite or at most countable number of states, and time running continuously.
In setting up a stochastic model for a collection of agents, then, we first choose a set of variables as a state vector for the model. The state vector should carry enough information about the model for the purpose at hand, so that we can, in principle, calculate the conditional distributions of future state vectors, given the current one. Put differently, we must be able to calculate the conditional probability distributions of the model state vector at least for a small step forward in time, given current values of the state vector and time paths of exogenous variables.
This dynamic aspect of the model is described by the master equation, which is introduced in Chapter 3. Briefly, the master equation is the differential (or difference) equation that indicates how the probability of the model being at some specific state at a point in time is changed by the inflows and outflows of the probability fluxes.
- Type
- Chapter
- Information
- Modeling Aggregate Behavior and Fluctuations in EconomicsStochastic Views of Interacting Agents, pp. 9 - 18Publisher: Cambridge University PressPrint publication year: 2001