Two individuals arc considering applying for jobs available at Company A and Com

Question

Two individuals arc considering applying for jobs available at Company A and Company B. Each company has exactly one job opening. Company A offers a monthly salary of 5,000 TRY while Company B offers 6,000 TRY per month. The individuals need to decide simultaneously about which job opening they will apply to, without talking to each other. They need to choose one. If only one of them applies to a company, then she gets the job. If they apply to the same job, then the company chooses one of them randomly with equal probability and the other remains unemployed. Assume that each individual wishes to maximize her own profit and is risk neutral. Mathematically formulate the game between these two individuals. Is there a strictly dominant strategy for any individual? Explain. Identify all the Nash equilibria (in pure and mixed strategies).

Explanation / Answer

a) Individual 2

Company A Company B

Individual 1 Company A 2500,2500 5000,6000   

Company B 6000,5000 3000,3000

b) No there is no dominant strategy fo any individual. If individual 1 chooses Comapny A, it is best for Individual 2 to choose Company B and if individual 1 chooses Company B, it is best for Individual 2 to choose Comany A.

Same holds true for individual 1 as well.

Thus no player has dominant strategy.

c) There are two Nash equilibria

1) Individual 1 chooses company A and individual 2 chooses companyB.

2) Individual 2 chooses company A and individual 1 chooses companyB.

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