$9.$ Collusive outcome versus Nash equilibrium

Consider a remote town in which two restaurants, All$-$You$-$Can$-$Eat Caf$$ and GoodGrub Diner, operate in a duopoly. Both restaurants disregard health and safety regulations, but they continue to have customers because they are the only restaurants within $80$ miles of town. Both restaurants know that if they clean up$,$ they will attract more customers, but this also means that they will have to pay workers to do the cleaning.

If neither restaurant cleans, each will earn $\backslash (\backslash$$ $15,000\backslash )$; alternatively, if they both hire workers to clean, each will earn only $\backslash (\backslash$$ $10,000\backslash ).$ However, if one cleans and the other doesn't, more customers will choose the cleaner restaurant; the cleaner restaurant will make $\backslash$$$19,000,$ and the other restaurant will make only $\backslash (\backslash$$ $5,000\backslash ).$

Complete the following payoff matrix using the previous information. $($Note: All$-$You$-$Can$-$Eat Caf$$ and GoodGrub Diner are both profit$-$maximizing firms.$)$

If All$-$You$-$Can$-$Eat Caf$$ and GoodGrub Diner decide to collude, the outcome of this game is as follows: All$-$You$-$Can$-$Eat Caf$$ and GoodGrub Diner

If both restaurants decide to cheat and behave noncooperatively, the outcome reflecting the unique Nash equilibrium of this game is as follows: All$-$You$-$Can$-$Eat Caf$\_,$ and GoodGrub Diner