Two coffee shops, A and B$,$ are competing in the same area and can either choose to Lower Prices or Keep Prices High. Lowering prices attracts more customers but reduces profit per sale. Here's their payoff matrix:

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|\}$

$\backslash$hline & $\backslash$begin$\{$tabular$\}\{$c$\}$

Coffee Shop B: $\backslash \backslash$

Lower Prices

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Coffee Shop B: $\backslash \backslash$

Keep Prices High

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$c$\}$

Coffee Shop A: $\backslash \backslash$

Lower Prices

$\backslash$end$\{$tabular$\}$ & $\backslash ((3,3)\backslash )$ & $\backslash ((9,1)\backslash )\backslash \backslash$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$c$\}$

Coffee Shop A: $\backslash \backslash$

Keep Prices High

$\backslash$end$\{$tabular$\}$ & $\backslash ((1,9)\backslash )$ & $\backslash ((7,7)\backslash )\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Which outcome represents the Nash equilibrium for this game?

$\backslash ((1,9)\backslash )$ where $\backslash ($ A $\backslash )$ keeps prices high and $\backslash ($ B $\backslash )$ lowers prices

$\backslash ((3,3)\backslash )$ where both lower prices

$\backslash ((9,1)\backslash )$ where $\backslash ($ A $\backslash )$ lowers prices and $\backslash ($ B $\backslash )$ keeps prices high

$\backslash ((7,7)\backslash )$ where both keep prices high