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.
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