Mathematical Strategies in the Military

Jayna Newman and Dane Wesenberg November 17, 2000

Readings:

"Mathematics and War" from Davis, Hersh and Marchisotto, The Mathematical Experience, Study Edition, Boston: Birkhauser, 1995 (pps. 101-104). (An overview of how mathematics has been involved in wars).

"Military Applications" Shubik, Martin, Game Theory in the Social Sciences. Cambridge, Mss: MIT Press, 1982 (ppsl 403-407). (Types of games used in war: Allocation games, duals, games of pursuit, and search)

"Deadly Games" Casti, John, Five Golden Rules. New York: John Wiley and Sons Inc. 1996 (pps. 3-8). (Real world example of using game theory in war).

"Real Worlds, Artificial Games" Casti, John Five Golden Rules. New York: John Wiley and Sons Inc. 1996 (pps. 40-41). (How games fit into real world applications).

Introduction:

John von Neumann was a very influential mathematician of his time. He was considerably involved in the cold war. Von Neumann was the inventor of game theory, which became a strategy and tool used to analyze war. The nuclear warfare strategy was based off von Neumann's ideas, which led to the doctrine of "mutually assured destruction." His mathematical calculations were used in making of the A-bomb and the H-Bomb. From his role with the computer, there are now simulations of war that are played out virtually.

Game theory is a mathematical model that is used to predict outcomes given certain constraints. There is a minimum of two players with different interests. Probability is taken into account to determine what the what the others players move would be, assuming each player chooses a rational move. Decisions are usually made without knowledge of the opponent's actions. Only a finite number of decisions is possible. Finally, there are payoffs, or incentives, to take certain risks in the game which would generate a higher score if one succeeds in the risk taken.

Discussion Topics:

1. Do you belikeve John von Neumann intended for his game theory and computer programming to be used?

2. If there would be a World War III, would it be considered a math war?

3. If there was a WWIII, a math war like described in the book, what would it be like?

4. Should war be like a game? Does the game take into account the lives at risk?

Schedule:

Introduction distributed by Tuesday, November 28, 2:50 PM

Individual initial posts by Sunday. December 3.

Open discussion period: Monday, December 4 to Tuesday, December 12.

Summary posted by, Thursday, December 14.