I was looking at the exercise $2$ in this file http://isites.harvard.edu/fs/docs/icb.topic1531493.files/Practice%20Problem%20Solutions%20on%20Nash%20Equilibrium.pdf pages 4 to 7.
I do not understand why at the exercise concludes without checking for all possible supports for player 2, as done for player 1.
Is it correct to consider only all possible supports of just one of the two players? If so, why? Also, it would be indifferent which of the two player is choosen?
If it is not in general enough to consider all the supports for just one of the two players, what makes it correct in that case? What do it in general?
2026-03-29 03:36:11.1774755371
Finding all mixed Nash equilibria in a $3\times 3$ game
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1
This is not specific to this specific problem or type of problem. Case analysis always works by covering a complete set of mutually exclusive cases, i.e. cases whose union includes all possibilities. Player $1$ must have some support; if you've covered all possible supports for player $1$, you've covered all possible cases. There's nothing deep or game-theoretic about that.