VIII. $(\backslash (19^\{+3\}\backslash$mathrm$\{$pts$\}\backslash ))$ The following is a payoff$/$penalty table for a two$-$person$-$zero$-$sum game.

$(8-$a$)(2$ pts$)$ If column player took strategy A and row player knew it$,$ then what strategy would row player take?

$(8-$b$)(2$ pts$)$ If row player took strategy $2$ and column player knew it$,$ then what strategy would column player take?

$(8-$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 $5$

Resulta $-----------$

Col Col

$```$

$```$

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?$)$

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

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

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

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

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