Question

Suppose there is a remote stretch of highway along which two restaurants, Last Chance Café 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 workersito do the cleaning. If nelther restaurant cleans, each will earn $10,000; alternatively, if they both hire workers to clean, each will eam only 57 , 000. Howevec, if one cleans and the other doesn't, more customers will choose the cleaner restaurant; the cleaner restaurant will make s15,000, and the other restaurant will make only $3,000. Complete the following payoff matrix using the information just given. (Note: Last Chance Cafe and Desolate Diner are both profic-maximizing firms.) If Last Chance Cafe and Desolate Diner decide to collude, the outcome of this game is as follows: Lost Chance Cafe and Desolate Diner If both restaurants decide to cheat and behave noncooperatively, the outcome reflecting the unique Nash equ librium of this game is as foliowst Last Chance Cafe and Desolate Diner

Answer 1

In a duopoly scenario between Last Chance Cafe and Desolate Diner, each faces the decision to clean or not comply with health codes. The Nash equilibrium suggests that both will choose not to clean to ensure a higher guaranteed profit, although collusion would lead to an equal distribution of higher profits if both invest in cleaning and comply with health regulations.

Step-by-step explanation:

The subjects at hand are game theory and business, particularly dealing with the concept of the prisoner's dilemma in a duopoly situation. This scenario involves two restaurants, Last Chance Cafe and Desolate Diner, which face a strategic decision about whether to comply with health codes. We have a scenario where their choices will determine their respective profits based on whether one or both decide to clean or not clean their restaurants. If both decide to clean up, they will each earn less than if neither cleans, due to costs associated with compliance. However, cleaning yields a higher payoff if the competitor does not clean.

If Last Chance Cafe and Desolate Diner decide to collude, both restaurants could potentially maintain health standards and share customers, leading to an agreed-upon equal profit for both. If they decide to cheat in a noncooperative manner, they will each earn a lower profit but avoid being outcompeted by the other.

The payoff matrix for this scenario would look like this:

• If both the people clean, each earns $7,000.
• If neither cleans, each earns $10,000.
• If one cleans and the other does not, the cleaner earns $15,000, and the non-cleaner earns $3,000.

Assuming rational profit-maximizing firms, collusion typically results in both parties agreeing to clean, understanding that mutual cheating would lead to less profit overall. However, without enforceable contracts or trust, the unique Nash equilibrium in this game is typically where both choose not to clean, as it guarantees a higher profit than being outcompeted by the other who cleans.