$(8-$c$)(9$ pts in total$))$ Answer the questions according to the following QM result on a $2-$person$-0-$sum game:

Module$/$submodule: Game Theory

Problem title: Test Problem $5$

Results $----------$

$$Col$$ Col$$

$$ strat A$$ strat B$$ Row Mix

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Row strat $16110\mathrm{.}375$

Row strat $2850\mathrm{.}625$

Column mix$0\mathrm{.}750\mathrm{.}25$

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Value of game $($to row$)=7\mathrm{.}25$

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$(8-$c$\mathrm{.}1)(5$ pts$)$ What is the equilibrium mixed strategy for row player in this game? $$Explain the meaning of the mixed strategy briefly $($i$.$e$.,$ what does that strategy mean?$)$

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$(8-$c$\mathrm{.}2)(2$ pts$)$ What is the equilibrium mixed strategy for the column player in this game? $($no explanation is needed$)$

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$(8-$c$\mathrm{.}3)(2$ pts$)$ What is the expected loss of the column player at equilibrium?

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$(8-$d$)(4$ pts$)$ If row player leaves his equilibrium strategy and uses a new strategy $\{0,1\},$ but column player stays with his equilibrium strategy, then

$(8-$d$\mathrm{.}1)$ what is the expected payoff of the row player?$$

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$(8-$d$\mathrm{.}2)$ If column player has identified the unilateral strategy change of row player, what would column player do for his best?

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$(8-$e$)(2+3$ pts$)$ Suppose both players leave their equilibrium mixed strategies.$$ The new strategy for row player is $\{1,0\}.$ The new strategy for column player is $\{0\mathrm{.}5,0\mathrm{.}5\}.$

$(8-$e$\mathrm{.}1)$ What is the value of the game with the new strategies? $($show your calculations$)$

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$(8-$e$\mathrm{.}2)$ Which player is better off with these changes of strategies?$$ Briefly explain.