Are there theorems for Agent Based Models

[Paul Johnson]

An economist said to me the other day, "where are your theorems? Aren't
there established results that guide modeling choices?"  I shrugged.

Here is an example of where there is probably a theorem, somewhere,
somehow.  Consider lots of agents who can observe the behavior of other
agents within a neighborhood and then adjust their behavior. 

Lately I've noticed you can write this kind of a simulation 2 ways.

1. Assume all agents survey the environment as it was after the last
time step.  If agents are in time 2, for example, they look around at
all other agents as they were at the end of time 1.  (Example:Heatbugs
heat display is updated once per time period, all agents refer to that
snapshot)  

2. Assume that all agent actions have "instantaneous effects" on each
other.  If we are in time 2, each agent who observes is able to see all
agent actions up to that instant.  If in time 2, a long list of agents
is called upon to act (possibly in random order), each one is aware of
the actions of the previous agents.  Agents who acted in step 2 before
are seen and their changes are taken into account.

These 2 approaches yield some initial differences in test models I've
been working on, but the effects seem to be short term.  

Is there a theorem that says something about the likelihood of
divergence in observations based on the 2 specifications?



-- 
Paul E. Johnson                       email: address@hidden
Dept. of Political Science            http://lark.cc.ukans.edu/~pauljohn
University of Kansas                  Office: (785) 864-9086
Lawrence, Kansas 66045                FAX: (785) 864-5700


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