I am very new to the game theory, however from videos on youtube I have been learning a bit. However, I am not sure how I can apply the knowledge to this question:
A and B person decide to apply for a job simultaneously. Meanwhile two companies open up a place for only one employee each. Salaries: $1/2*x < y < 2*x$ where x and y are companies respectively. If a workplace will have only one applicant, they will hire, otherwise decision will be made at random and the unsuccessful applicant will no longer be able to apply at another company, therefore the benefit would equal to 0, Find all the balances against Nash in pure game strategies
I guess I begin this way, however in the $Row1-Col1$ cell I cannot tell which one will be accepted, nor can I say about cell $Row2-Col2$. Also, none of the salaries actually seem larger than the other one, thus how would I know which would be the most desired for these guys. Only I can tell is that most profitable strategies would be $Row1-Col2$ OR $Row2-Col1$.
How should I progress?