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# Game Theory : Two Person Zero Sum Game

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Two armies are advancing on two cities. The first army has 4 regiments and the second army has 3 regiments. At each city, the army that send more regiments to the city captures both the city and the opposing army regiment. If both armies send the same number of regiments to a city, them the battle at the city is a draw. Each army scores 1 point per city captured and 1 point per captured regiment. Assume that each army wants to maximize the difference between its reward and its opponent's reward. Formulate this situation as two-person zero-sum game and solve for the value of the game and each player's optimal strategies.

https://brainmass.com/math/discrete-math/game-theory-two-person-zero-sum-game-88053

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Game Theory: Formulate Problem as a Two-Person Zero-sum Game

Problem -
• Two armies comprised of Battalions (Bns) advance on Cities
o Red Army has 4 Bns
o Blue Army has 3 Bns
• At each city the Army that sends the most Bns wins the city and captures the troops
• Each Army scores 1 point for each city won, and 1 point for each Bn captured
• Assume each Army wants to Maximize difference between its reward and the other armies reward
• Formulate Problem as a Two-Person Zero-sum Game
• Solve for value of game and each army's optimal strategy.

Red and Blue army Bns will be called Reds and Blues respectively from now on.
The cities will be named A and (you guessed it) B.

We will make some assumptions to start:

1. Armies not assigned to A will be assigned to B (e.g. 2 Reds go to A and 2 Reds go to B - no reserves).
2. We will develop the table for the number of armies sent to A, but the points earned will be for the conflict at both ...

#### Solution Summary

A two person zero sum game is investigated.

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