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There is a zero sum game G where player one plays T and Player two plays y and z. However y dominates z and Nash Equilibrium in this game would be (Ty). How can I prove this? Is it possible with minimax theorem or brower fixed point theorem

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It suffices to exhibit an example, such as $$\begin{array}{|c|c|} \hline 1 & 1 \\ \hline 1 & 0 \\ \hline \end{array}$$ Here, 1 plays the top row and 2 plays (indifferently) the left or the right column, but the left column is weakly dominated by the right column.

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  • $\begingroup$ Will this example work in zero sum game? $\endgroup$ – user_2334 Mar 19 '17 at 9:06
  • $\begingroup$ It is a zero-sum game. $\endgroup$ – mlc Mar 19 '17 at 9:39
  • $\begingroup$ 1 only plays T out of two possible choices :-) $\endgroup$ – mlc Mar 19 '17 at 9:45
  • $\begingroup$ If you prefer, delete the second row and you have a trivial game (where 1 has no choice to make) that satisfies your question. To my taste, this second solution is less attractive because 1 is not really playing. $\endgroup$ – mlc Mar 19 '17 at 9:46
  • $\begingroup$ No thanks. This is getting close to private tutoring. Good luck on your HW. $\endgroup$ – mlc Mar 19 '17 at 10:31

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