A mathematical formalism for agent-based modeling
  Many complex systems can be modeled as multiagent systems in which the constituent entities (agents) interact with each other. The global dynamics of such a system is determined by the nature of the local interactions among the agents. Since it is difficult to formally analyze complex multiagent systems, they are often studied through computer simulations. While computer simulations can be very useful, results obtained through simulations do not formally validate the observed behavior. Thus, there is a need for a mathematical framework which one can use to represent multiagent systems and formally establish their properties. This work contains a brief exposition of some known mathematical frameworks that can model multiagent systems. The focus is on one such framework, namely that of finite dynamical systems. Both, deterministic and stochastic versions of this framework are discussed. The paper contains a sampling of the mathematical results from the literature to show how finite dynamical systems can be used to carry out a rigorous study of the properties of multiagent systems and it is shown how the framework can also serve as a universal model for computation. 
Reinhard Laubenbacher, Abdul S. Jarrah, Henning Mortveit, and S.S.   Ravi