The simulations by Robert Axelrod and biologist W.D. Hamilton attempting to demonstrate the evolution of cooperation  use multi-agent simulations in an attempt to show that within an environment where agents can either cooperate or cheat with repeated outcomes the best strategy under many circumstances is to cooperate. This type of simulation is uniquely powerful in that it evaluates many competing strategies ultimately identifying one that works under a well-defined scenario.
Multi-agent simulations are appealing in that they allow researchers to generate data and evaluate scenarios that are rich and complex and potentially more similar to that of the “real world”. Within a multi-agent simulation each agent acts with its own strategy. That strategy can either be a common objective or an individual objective.
These types of simulations might be effectively deployed to explain the behaviors of ants. Each individual ant has a relatively simple set of commands. By simulating many competing commands and evaluating the effectiveness of different types of ants at building colonies within a rich environment it could be informative.
Within applied economics multi-agent simulations often have a spatial component that is used to identify placement and relation of agents within the environment. Other relational scales may be appropriate as well. If looking at social network analysis it may be useful to have both a spatial as well as shared public spaces networks in which agents can interact.
One of the most challenging aspect of multi-agent simulations is the inherent complexity of the environment and the interactions that agents are making. Often times, though you have defined the environment and the strategies of agents it is not clear exactly how those strategies interact with the environment to produce the results that they do.
In a way this is the point. Multi-agent simulations can demonstrate results that are otherwise difficult to demonstrate purely through math or argumentation. But, as such it is often difficult to be sure what mechanisms are driving the results that are being produced: because of the agents’ actions, the environmental variables, or some other artifact not previously considered.
As such, care in interpretation and rigorous error checking are extremely routines when designing and evaluating simulations.