Description

This book analyses how a large but finite number of agents interact and what statistical consequences follow. How do a large but finite number of agents interact, and, consequently, what macroeconomic statistical regularities or patterns may evolve? The book examines situations (e.g. fluctuations about equilibria, multiple equilibria and asymmetrical cycles of models) which are caused by model states stochastically moving from one basis of attraction to another. How do a large but finite number of agents interact, and, consequently, what macroeconomic statistical regularities or patterns may evolve? The book examines situations (e.g. fluctuations about equilibria, multiple equilibria and asymmetrical cycles of models) which are caused by model states stochastically moving from one basis of attraction to another. This book has two components: stochastic dynamics and stochastic random combinatorial analysis. The first discusses evolving patterns of interactions of a large but finite number of agents of several types. Changes of agent types or their choices or decisions over time are formulated as jump Markov processes with suitably specified transition rates: optimisations by agents make these rates generally endogenous. Probabilistic equilibrium selection rules are also discussed, together with the distributions of relative sizes of the bases of attraction. As the number of agents approaches infinity, we recover deterministic macroeconomic relations of more conventional economic models. The second component analyses how agents form clusters of various sizes. This has applications for discussing sizes or shares of markets by various agents which involve some combinatorial analysis patterned after the population genetics literature. These are shown to be relevant to distributions of returns to assets, volatility of returns, and power laws. 1. Overview; 2. Setting up dynamic models; 3. The master equation; 4. Introductory simple and simplified models; 5. Aggregate dynamics and fluctuations of simple models; 6. Evaluation of alternatives; 7. Solving non-stationary master equations; 8. Growth and business cycle models; 9. Example: a new look at the diamond search model; 10. Interaction patterns of agents and distributions of cluster sizes; 11. Example: share markets with two dominant types of participants in a market. 'This is a most welcome treatment of stochastic dynamics in economic models, and its significance for theoretical and applied economics … Professor Aoki has provided a self-contained description of all necessary and relevant concepts of the modelling toolbox, including key stochastic dynamics concepts such as the Master Equation (the backward Kolmogorov-Chapman Equation), the Fokker Planck equation, Jump Markov Processes, Random Partitions and Combinatorial Randomness.' Asia Pacific Journal of Management 'Once again Masanao Aoki has written a book ahead of its time. This time he applies techniques popular in the hard sciences, but alien to most economists, to analyse the dynamic interaction of a large (finite) number of agents (or entities.) He characterises types of agents by their decisions and the movement between types as endogenous transition probabilities. Aoki uses random combinatorial analysis to describe the distribution of types, and the backward Chapman-Kolmogorov equations to describe the aggregate dynamics. This is an innovative approach to characterise a complicated dynamic stochastic economic environment.' Rog