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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.

This book contributes substantively to state-of-the-art macroeconomic modeling by providing a method for modeling large collections of heterogeneous agents subject to non-pairwise externality called field effects, i.e. feedback of aggregate effects on individual agents or agents using state-dependent strategies. Adopting a level of microeconomic description which keeps track of compositions of fractions of agents by 'types' or 'strategies', time evolution of the microeconomic states is described by (backward) Chapman-Kolmogorov equations. Macroeconomic dynamics naturally arise by expansion of the solution in some power series of the number of participants. Specification of the microeconomic transition rates thus leads to macroeconomic dynamic models. This approach provides a consistent way for dealing with multiple equilibria of macroeconomic dynamics by ergodic decomposition and associated calculations of mean first passage times, and stationary probabilities of equilibria further provide useful information on macroeconomic behavior.

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