Formal specification of multi-agent e-barter systems

An e-barter multi-agent system consists of a set of agents that exchange goods. These agents may perform multilateral exchanges involving several goods. In particular, money can be one of these goods. Each agent is endowed with a utility function indicating the preferences of the respective user. In order to improve the performance, these barter systems are structured in a hierarchical form. Initially agents are grouped, according to localities, into local markets. Once a local market gets completed, that is, no more exchanges are possible, the local market itself becomes a new agent. The preferences of this agent, given by a new utility function, represent the individual preferences of its former customer agents. Then, local markets exchange goods in a higher order market until it gets completed. The process is iterated, in a bottom-up fashion, until the global market embracing all the agents in the system gets completed as well. We provide a formal language, based on classical process algebras, for specifying and analyzing e-barter systems. We also study properties of e-barter systems represented in our notation. In particular, we show that the final distribution of goods in a hierarchical e-barter system is a Pareto optimum. In other words, we will be able to prove that economic efficiency is not lost by considering our hierarchical structure instead of a single market.