Game Theory and System Dynamics

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zenabraham@aol.com
Junior Member
Posts: 14
Joined: Fri Mar 29, 2002 3:39 am

Game Theory and System Dynamics

Post by zenabraham@aol.com » Tue Apr 02, 2002 11:43 am

Hello,

What examples are there of the matting of SD with common studies in Game
Theory? For example, are there works featuring the graphing of equations
using models developed in STELLA?

___________________________________________________________________
Zenophon Abraham
From: zenabraham@aol.com


"Andy Ford"
Junior Member
Posts: 14
Joined: Fri Mar 29, 2002 3:39 am

Game Theory and System Dynamics

Post by "Andy Ford" » Tue Oct 08, 2002 2:25 pm

Folks,

This is Andy Ford responding to Zena Abrahams question about game theory
and system dynamics modeling. Dong-Hwan Kim and Doa Hoon Kim write about a
system dynamics model of car drivers and the policemen that issue traffic
violations in the Spring 1997 issue of the SYSTEM DYNAMICS REVIEW. They use
the SD model to show that "it takes a very long time for a game-theoretic
equilibrium to appear."

Andy Ford
From: "Andy Ford" <FordA@mail.wsu.edu>
Program in Environmental Science & Regional Planning
Washington State University
Pullman, WA 99164-4430

"Michael Bean"
Junior Member
Posts: 14
Joined: Fri Mar 29, 2002 3:39 am

Game Theory and System Dynamics

Post by "Michael Bean" » Wed Oct 09, 2002 7:44 am

Zennie,

Theres a paper and simulation that I wrote last year titled "Anatomy of a Price War" that combines
game theory and system dynamics to understand price wars. The paper uses the popular game theory 2 x
2 matrix to examine the challenges faces PC makers competing with Dell and then uses causal diagrams
to enhance the understanding of the price war.

The paper, titled "Anatomy of a Price War" can be read at:
http://www.forio.com/pricing20010912.htm

The simulation based on the paper can be run at:
http://broadcast.forio.com/sims/pricing/index.htm

And the model used to develop the simulation can be viewed and copied at:
http://broadcast.forio.com/sims/pricing/viewmodel.htm

Best regards, Michael Bean
___________________
Forio Business Simulations
mbean@forio.com

"J Mukherjee"
Junior Member
Posts: 14
Joined: Fri Mar 29, 2002 3:39 am

Game Theory and System Dynamics

Post by "J Mukherjee" » Sun Oct 13, 2002 9:32 pm

My Ph. D. work (1996, Univ of Illinois, Urbana-Champaign) involved numerical
solutions of dynamic games based on system dynamics models. More on this may
be found on my website at
http://www.optimlator.com

Also, keyword search of "game" or my name on the SD mailing list archive
(through the above website) will bring you to details of this and further
references.

I found Kesten Greens remarks interesting, especially his comment that
neither the experts nor the game theory provided good results. In my own
work what I had found was that game-theoretic solutions of even very small
problems were mathematically (no closed-form solutions!!) and numerically
(2-point boundary-value problems!!) difficult. I had also been impressed by
the power of system dynamics simulations to provide insights. The only
problem was that any realistic problem (not academic text-book type
exercises) demanded either too many simulations with SD models (now Vensim I
believe has tools to help with this aspect), which meant subjective
(consultant-induced?) bias could creep in, giving SD a bad name, or we would
be forced to develop very small game-theory solutions which would solve only
ivory-tower academic problems, not the realistic ones we wanted to solve in
the first place.

That is when I had coined the term "optimlation". The grand idea, in my
wide-eyed youthful enthusiasm, was that repeated optimizations (finding
optimal dynamic game-theory solutions) for players facing different
scenarios (represented by simulations on SD models created by perturbations
to the system by parametric changes) would lead to the best possible
practical solutions to complex problems. The idea was to use optimization in
the manner simulation has been used so far. Hence optim(izing) (simu)lations
or optimlations.

The best example of this I have found is in martial arts - fighting on the
street is complex and chaotic (this logic will apply to military strategy
too so far as I know). To win on the street, martial artists do a lot of
simulations (practice, practice, practice!!!) The bad news is that old age
and smarter street technologies catch up with you and simulation hits limits
very quickly. Then the focus becomes optimizations (refinement, refinement,
refinement!!) while "practicing" simulations as a way of life (budo, way of
the warrior). In this case, in my view, a martial artist lives the life of
continuous optimlations rather than just simulations (sparring practice all
the time with injured joints and bones) or optimizations (kata practice akin
to theoretical mathematics). My hunch is that Kesten Greens "simulated
interactions" in which players are trying to optimize something while
dealing with different scenarios (simulations) are similar to
"optimlations". [My ideas were/are developed in aikido practice, though I am
sure other artists will find similarities].

On prediction and usefulness, in Hillier and Liebermans Operations Research
text, their finding was that statistics was the best predictor/most useful,
followed by LP and some other techniques. Nonlinear programming and game
theory were way last and system dynamics was not even mentioned (nor was
"optimlation" :-< the word had not been coined then) These results may be
different now as I am recalling stuff from a while back.

Would love to hear from Kesten what he thinks of this -

Regards

Jaideep

Jaideep Mukherjee, Ph. D.
From: "J Mukherjee" <jaideep@optimlator.com>
www.optimlator.com

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