scottshambaugh

Joined 6 years ago

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Comment · 4 months ago
Comment · 5 months ago
Thanks for sharing! My background is in control theory, and I think the links between it and game theory and dynamical systems in general are super fruitful but woefully underexplored. Writing this was a good excuse to brush up on my linear algebra basics again.
Comment · 5 months ago
I had the computer do it for me :)

Really though, the way to do this is to represent each game as a payout matrix A, which for this category of game will be skew-symmetric with -1/0/+1 entries. Then since this is a symmetric zero-sum game, you find the null space of that matrix, impose the constraint that probabilities must sum to 1 and individually be >= 0, and that gives you the endpoints of the Nash Equilibria. The optimal strategies (could be one unique one for odd n!) lie on the convex hull of those points.

Comment · 8 months ago
Comment · 8 months ago
Comment · 8 months ago
Comment · 11 months ago

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