notes-math-gameTheory-gameTheoryNotes

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my guess-y first step towards a proof of the Nash Existence Theorem:

We are given a finite set of pure strategies. Choose one, call it the 'current strategy'. Iterate through all of the others, is there any other one that dominates it? If so, make it the current strategy, and repeat. Since there are finitely many pure strategies, either eventually you will find a pure strategy which is not dominated by any others (in which case it is a Nash equilibria), or you will find a cycle. If you found a cycle, take all the pure strategies in the cycle and form a mixed strategy which has an equal weight to each of the pure strategies in the cycle.

(i think this doesn't completely work because i didn't account for things which are <= instead of dominating, and also, domination is of course not transitive so what about comparison between arbitrary 'chords' across the cycle? for the latter concern, mb now just continue to iterate, as if the new mixed strategy were an additional pure strategy?)

note: (most of) the actual proof is here: http://www.cs.ubc.ca/~jiang/papers/NashReport.pdf

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