Agent-based modeling in Economics by Process Algebra

Stochastic process algebra have been successfully used to analyze performance of software systems and correctness of communication protocols. While expressive, stochastic process algebra models of realistic systems give rise to Markov chains whose size is exponential in the length of the model, a phenomenon known as state-space explosion problem. Lumpability and fluid limits are two techniques which have proven effective in tackling this challenge. In this context, lumpability can be seen as an intermediate representation between the original (i.e., unaggregated) state space of a process and its fluid interpretation. This purpose has been served thus far by an equivalence relation called strong equivalence, which allows one to reduce the original Markov chain to a smaller, lumped Markov chain. This paper begins by reviewing PEPA++, an extension of the stochastic process algebra PEPA where minimum-based semantics are supplemented by product-based ones. Afterwards, we introduce the notion of exact equivalence and argue that it provides a tighter relation between the unaggregated Markov chain and the fluid representation, compared to the common notion of strong equivalence. Moreover, the paper devises a process algebra model whose fluid limit is shown to be the Goodwin model from economics. Exploiting the agent-based view, the paper derives a compact stochastic model of a single worker that is part of the worker population. This allows to study efficiently stochastic properties that escape the macroscopic view of Goodwin’s model.