The following payoff table depicts service competition between two hospitals in
ID: 1177211 • Letter: T
Question
The following payoff table depicts service competition between two hospitals in a southeastern city. (Each payoff represents profits in millions of dollars.) <?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />
Hospital B%u2019s Services
Basic
All-Purpose
Specialty
Basic
5; 7
5; 4
12; 6
Hospital A%u2019s Services
All-Purpose
4; 5
8; 7
7; 4
Specialty
6; 10
3; 12
3; 3
Questions:
a. Does Hospital A have a dominant strategy? If yes, what is it?
b. Does Hospital B have a dominant strategy? If yes, what is it?
c. Assuming hospitals A and B determine their strategies independently of one another, what are the hospitals%u2019 respective (Nash) equilibrium strategies? [HINT: Using the method of circles and squares may help you answer this question].
d. Suppose instead that the hospitals merge and, therefore, coordinate their service decisions. Which actions should they take? Explain briefly.
e. What general economic reasons might there be for a hospital merger to generate an increase in total profit? Would the hospitals%u2019 customers be likely to benefit from the merger? Under what circumstances? Explain carefully.
Hospital B%u2019s Services
Basic
All-Purpose
Specialty
Basic
5; 7
5; 4
12; 6
Hospital A%u2019s Services
All-Purpose
4; 5
8; 7
7; 4
Specialty
6; 10
3; 12
3; 3
Explanation / Answer
The following payoff table depicts service competition between two hospitals in a southeastern city. (Each payoff represents profits in millions of dollars.)
Hospital B Services
Basic
All-Purpose
Specialty
Basic
5; 7
5; 4
12; 6
Hospital A Services
All-Purpose
4; 5
8; 7
7; 4
Specialty
6; 10
3; 12
3; 3
Questions:
a. Does Hospital A have a dominant strategy? If yes, what is it?
When B provides Basic services A is best off providing Specialty services as A gets the highest payoff of 6 from doing so.
When B provides All Purpose services A is best off providing All Purpose services as well. A gets the highest payoff of 8 from doing so.
When B provides Specialty services A is best off providing Basic services as A gets the highest payoff of 12 from doing so.
Hence As best response to each of Bs action varies. Thus A does not have a dominant strategy.
b. Does Hospital B have a dominant strategy? If yes, what is it?
When A provides Basic services B is best off providing Basic services as B gets the highest payoff of 7 from doing so.
When A provides All Purpose services B is best off providing All Purpose services as well. B gets the highest payoff of 7 from doing so.
When A provides Specialty services B is best off providing All Purpose services as B gets the highest payoff of 12 from doing so.
Hence Bs best response to each of As action varies. Thus B does not have a dominant strategy.
c. Assuming hospitals A and B determine their strategies independently of one another, what are the hospitals%u2019 respective (Nash) equilibrium strategies? [HINT: Using the method of circles and squares may help you answer this question].
The Nash equilibrium is the set of actions where neither Hospital will want to deviate unilaterally to another action. Such a pair will have both payoffs highlighted in yellow, i.e. that action taken by each Hospital is a best response to the action taken by the other.
Here, the Nash equilibrium is the set of action [All Purpose, All Purpose], i.e. both A and B choose to provide All Purpose services.
d. Suppose instead that the hospitals merge and, therefore, coordinate their service decisions. Which actions should they take? Explain briefly.
When the hospitals merge, their objective is to maximize the sum of payoffs. In this case, the merged hospital will decide to provide Specialty Services at B and Basic Services at A. The total payoff is 18, which is the highest among the set of actions available.
e. What general economic reasons might there be for a hospital merger to generate an increase in total profit? Would the hospitals%u2019 customers be likely to benefit from the merger? Under what circumstances? Explain carefully.
A hospital may decide to merge to cut down on costs. Each branch of medicine requires its own set of instruments and staff. If two hospitals under the same management provide the same set of services, the hospital can cut down on costs by allowing one of them to provide specialized services while the other covers the rest. Splitting the functions between the two can also make management and oversight simpler.
The merger can be beneficial to customers since now one of the hospitals is providing specialized care while the other offers Basic services. This can be beneficial in a scenario where the population suffers from certain diseases or disorders which require advanced care. The services provided by an All Purpose Hospital could be inadequate in this case. The merger can also reduce the cost of health care.
Hospital B Services
Basic
All-Purpose
Specialty
Basic
5; 7
5; 4
12; 6
Hospital A Services
All-Purpose
4; 5
8; 7
7; 4
Specialty
6; 10
3; 12
3; 3
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