Instruction

1. You select the probability of troop concentration (Blue) with clicks on the blue scale.

2. You do the same for Red.

3. You click on the visible (Blue) commanding officer, who selects the Blue decisions according to the probabilities decided by you via the blue scale. (At the same time, the invisible Red commanding officer makes the corresponding decisions according to the red scale probabilities.)

4. The simulation continues as long as you like. Each time, new decisions are taken by both participants according to the frequences you have decided.


The optimal mixed strategy decision problem and the army

The problem comes from classical game theory, the distribution of resources (such as army platoons) when you have an opponent (enemy).

Problems of this type are often called "Blotto games". Some important decision problems of Colonel Blotto are presented by Washburn (1994).

You do not know how the opponent will distribute his resources (Red army platoons) and the opponent does not know how you will distribute your resources (Blue army platoons).

It is possible to calculate the (Nash) equilibrium frequences of resource concentration levels in different areas.
Nash obtained the "Nobel price in economics" for his game theory findings.
In Nash equilibrium, no participant in the game benefits from changing frequences as long as the opponent does not deviate from the Nash equilibrium frequences.

Here, you may read more about these central and important decision problems and learn how to determine the optimal frequences of different decisions: Lohmander, P., Hemvärnet vinner på spelteori, Hemvärnet #1, 2004,
http://www.hemvarnet.mil.se/hemvarnet/attachments/0401_22-24.pdf
(Direct link to presented software: http://www.lohmander.com/MIL/ResFStri.doc )

Here is the software which you may use to determine the Nash equilibrium frequences (in Swedish):
http://www.lohmander.com/mil/2pzsg/taktik_PL_1.htm


Have a nice evening!

        Peter Lohmander
http://www.Lohmander.com


References:

Lohmander, P., Optimal decentralized tactical decisions of isolated blue units behind red lines, (Abstract book), New Opportunities for Operations Research, EURO/INFORMS (= The Association of European Operational Research Societies / Institute for Operations Research and the Management Sciences), Military Operations Research Cluster, Istanbul, July 06-10, 2003. Link: http://www.istanbul2003.org Connected information: http://www.lohmander.com/mil/MilDir.html

Lohmander, P., Hemvärnet vinner på spelteori, Hemvärnet #1, 2004,
http://www.hemvarnet.mil.se/hemvarnet/attachments/0401_22-24.pdf (Direct link to presented software: http://www.lohmander.com/MIL/ResFStri.doc )

Washburn, A.R., (1994) Two person zero sum games, Topics in Operations Research, INFORMS, Institute for Operations Research and the Management Sciences

http://www.lohmander.com/mil/MilDir.html

http://www.lohmander.com/mil/ResFStri.html

http://www.lohmander.com/mil/OriResFStri.html

http://www.lohmander.com/mil/DarkArm.doc

http://www.lohmander.com/mil/Tactical7.doc

http://www.lohmander.com/mil/NashLP2.doc

http://www.lohmander.com/mil/2pzsg/taktik_PL_1.htm

http://www.lohmander.com/mil/EUROInf03.doc