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Two-Person Zero-Sum Game Problem

Need help setting up this 3X4 Matrix problem. I have only worked 2X2 matrix game problems per recent homework, however, I can't seem to leverage that knowledge for this problem. I'm also not sure how to deal with the extra reward variable (one point for capturing each of the other army's bn). Also need help setting up the LP for the Army with 4 Battalions. Thank You!

Based on questions from OTA's, here is additional input I neglected earlier. Sorry!

- How many cities? two
- What happens when Armies send the same number of Battalions? it is a draw, i.e., no points


Solution Summary

This solution is comprised of a detailed explanation to answer how many cities.