Challenge Set #$3$

Instructions:

These problems will ask you to use the pieces of knowledge we discussed through multiple classes. The

goal is to really push your ability to take ideas we learn in class and properly apply them. You are allowed

to state your assumptions and approach the questions using any techniques you want. Assumptions that

change the questions or change fundamental economic concepts won't be allowed. You will be graded on

your ability to use economic theory to solve problems, communicate how you solved them, and$/$or convince

me that it is the correct answer. Math, graphs, and economic intuition are all valid ways to communicate.

Just be clear on what you are doing.

Background Information

In Florida, prior to $2019,$ any new healthcare facility must have a Certificate of Need $($CON$)$ in order to

operate. Thus, if an entrant wants to enter the market in Florida, they must apply for a CON with the state

government. After applying for a CON, any incumbent healthcare facility may invest resources to research

and lobby to explain why the CON should be denied. Sometimes in a given year, the state government is

very stingy with CON and if any incumbent opposes the CON, the state will instantly deny the entrant

from entering. In other years the state government is loose with CON and approves any CON no matter if

an incumbent denies it or not.

If an entrant decides not to apply for a CON, they don't lose anything, the incumbent maintains monopoly

power. If the entrant applies and is approved, the profits are split. In order to apply, an entrant must break

ground and begin construction. If the entrant applies and is denied, then the entrant loses the resources

from denied entry while the incumbent maintains monopoly power minus the cost of lobbying.

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Scenario $1$

Assume the incumbent knows the state government is stingy with CON approvals or loose with CON approvals. The payouts are as follows:

a$)$ Find Bayes Nash Equilibrium.

Scenario $2$

Suppose hnth narties know the state of the world See navnffs as follows.

a$)$ Find the Nash Equilibrium for each Nature type. That is to say, if stingy, what is the NE$?$ If Loose, what is the NE$?$

b$)$ Given that nature is random, what is the expected value for Entrants playing this game? What is the expected value for Incumbents playing this game?

Scenario $3$

Assume both Entrant and Incumbent don't know whether the State government is Stingy or Loose. The payout is as follows

Do not solve for a Nash Equilibrium

a$)$ How does this game differ from Scenario $1$ with respect to the set of strategies the Incumbent now plays?

b$)$ Assume you are the incumbent. What strategy should you choose if your goal is to try to induce the Entrant to "Not Apply"?

c$)$ Assume the Entrant is risk neutral, is your strategy from part $($b$)$ a credible threat? Explain

d$)$ Assume the Entrant is risk averse, is your strategy from part $($b$)$ a credible threat? Explain

Questions

Q$1)$ Assume we are in Scenario $1$ where the incumbent knows the Nature, but the entrant does not. If the

incumbent can communicate with the entrant, would it benefit the Incumbent to tell the Entrant? $($Another

way to think about this, would the incumbent rather play the game in Scenario $1$ or Scenario $2?)$

Q$2)$ Suppose the Incumbent can induce the Entrant to have the strategy "Not Apply" in Scenario $3.$ Would

the Incumbent prefer playing this game over Scenario $1?$ Would the Incumbent prefer playing this game

over Scenario $2?$

Q$3)$ Rank order which scenarios would the incumbent prefer. Rank order which scenarios the entrant

would prefer.

Please answer all question and explain the steps to me as well. Thank you very much.