Homework $($Ch $17)$

$8.$ Collusive outcome versus Nash equilibrium

Suppose there is a remote stretch of highway along which two restaurants, Last Chance Caf$$ and Desolate Diner, operate in a duopoly. Neither restaurant invests in keeping up with health code regulations, but regardless they both have customers as they are the only dining options along a $79$mile portion of the road. Both restaurants know that if they clean up and comply with health codes 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 $$13,000$; alternatively, if they both hire workers to clean, each will earn only $$10,000.$ However, if one cleans and the other doesn't, more customers will choose the cleaner restaurant; the cleaner restaurant will make $$17,000,$ and the other restaurant will make only $$5,000.$

Complete the following payoff matrix using the information just given. $($Note: Last Chance Caf$$ and Desolate Diner are both profit$-$maximizing firms.$)$

Desolate Diner

If Last Chance Caf$$ and Desolate Diner decide to collude, the outcome of this game is as follows: Last Chance Caf$$ Diner $$ and Desolate If both restaurants decide to cheat and behave noncooperatively, the outcome reflecting the unique Nash equilibrium of this game is as follows: Last Chance Caf$,$ and Desolate Diner $$