Theorems for Agent Based Models

[Chris Landauer]

hihi -

there are a couple of other styles of agent update that are relevant to Paul's
question about theorems

the first one is whether the updates are synchronous or asynchronous (that is,
does the update cycle go through all the agents in the same order before going
to the next update cycle, or does it update agents at possibly different rates
that depend independently only on the agent being updated)

the next one is whether the agent cycle in the synchronous case goes through
the agents in the same order each time or not

the two alternatives in the original question were about whether the agent
update takes into account updates that have already occurred for agents that
have already been processed in the cycle, or always uses the values from the
previous cycle (the latter, for example, is the rule in Conway's Game of Life)

in both cases, the original question assumed the synchronous case above, so
that the updates in each time step are separated from those in other time
steps - even so, if the order of the agent updates is randomly selected at
each step, then the activity is much more like the asynchronous case

it can be proved (i believe) that the asynchronous case and the synchronous,
random update ordering case will have similar behaviors in the long run - for
example, they almost never get into loops, whereas the synchronous, same order
case can get into loops in its behavior (e.g., the GoL), and often does get
into many small loops (especially when the agent interaction rules require
proximity, as the GoL does)

there are theorems also about the asynchronous case that relate its behavior
to that of markov chains, thereby providing a lot of computable information
about their asymptotic behavior

most of these theorems are well-known in the discrete event simulation and
stochastic process literature, and some of them date back to the early part of
this century, though i haven't seen an explicit reference to their application
in this context

in short, yes it matters, and the actual situation is more interesting and
complicated than it might seem at first

more later,
cal

Dr. Christopher Landauer
Aerospace Integration Science Center
The Aerospace Corporation, Mail Stop M6/214
P.O.Box 92957
Los Angeles, California 90009-2957, USA
e-mail: address@hidden
Phone: +1 (310) 336-1361


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