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# Game Theory : Two-person, Constant-Sum Games

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The attached file has a problem that I can't figure out how to set up. Can you take a look and explain how this problem should be set up?

There are two people playing a two-person constant-sum game. Player 1 wants to travel from New York to Dallas using the shortest of the possible routes listed below. Player 2 has the ability to block one route out of Atlanta and one route out of Nashville. Player 1 will not know which roads are blocked until the arrival at Atlanta or Nashville. Should Player 1 start towards Atlanta or Nashville? Which routes should Player 2 block?

Route Length of Route
(miles)
New York -Atlanta 800
New York -Nashville 900
Nashville-St. Louis 400
Nashville-New Orleans 200
Atlanta-St. Louis 300
Atlanta-New Orleans 600
St. Louis-Dallas 500
New Orleans-Dallas 300

Complete routes Total
1. New York Atlanta St. Louis Dallas
800 300 500 1600
2. New York Atlanta New Orleans Dallas
800 600 300 1700
3. New York Nashville St. Louis Dallas
900 400 500 1800
4. New York Nashville New Orleans Dallas
900 200 300 1400

I don't see how to set up the table for the game? Can you show/explain it to me?

##### Solution Summary

Possibilities in a two-person, constant-sum game are investigated.

##### Solution Preview

The player I tries to minimize his traveling distance while player
II tries to maximize I's distance.

The table is as follows
a b c d
NY 1700 1600 1600 1600

NA 1400 1400 1400 1800

where the label of row denotes the direction player I chooses and
the label of column ...

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