Re: Are there theorems for Agent Based Models

[Rick Riolo]

I believe the references Sven has in mind are as follows:

Original paper:

Evolutionary games and spatial chaos.
  Nowak, Martin and May, R.M.
  Nature, 359, pp826-929.

Huberman and glance critque:

Evolutionary Games and Computer Simulations.
  Huberman, Bernardo A. and Glance, Natalie S.
  Proc. Natl. Acad. Sciences (USA), 90, 7716-18 (1993).

Nowak and May respond at length:

Spatial games and the maintenace of cooperation.
  Nowak, Martin, Bonhoeffer, S. and May, R.M.
  PNAS (USA), v91, pp4877-4881.  1994.

Huberman and glance's caution about using synchronous
updating (which is basically what is was all about)
has also been made in other contexts about 
CA (cellular automata) type models, e.g., Scott Page
has a paper about different update-order mechanisms.

- r


Rick Riolo                           address@hidden
Center for Study of Complex Systems (CSCS)
4477 Randall Lab                
University of Michigan         Ann Arbor MI 48109-1120
Phone: 734 763 3323                  Fax: 734 763 9267
http://www.pscs.umich.edu/PEOPLE/rlr-home.html

On Mon, 12 Jul 1999, Sven N. Thommesen wrote:

> Date: Mon, 12 Jul 1999 15:37:05 -0500
> From: Sven N. Thommesen <address@hidden>
> Reply-To: address@hidden
> To: address@hidden
> Subject: Re: Are there theorems for Agent Based Models
> 
> 
> I believe Huberman and Glance had a paper where they investigated just this
> difference, and they discovered that doing it in way #2 overturned previous
> results achieved with way #1. Their conclusion was that it makes a Big
> Difference how you arrange the order of actions.
> 
> I'll dig out the reference if you need it.
> 
> -Sven
> 
> At 03:27 PM 7/12/1999 -0500, you wrote:
> >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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