$3.$ Individual Problems $15-4$

After graduation, you enter salary negotiations for your first job. Suppose the potential employer $($employer A$)$ has two choices: to offer you a high salary or to offer you a low salary. You may then accept or reject whatever offer is made. The payoffs, as well as the decision tree, are depicted in the following figure.

Employer

High Offer

Low Offer

Employee Accept

Employee: $90$

Employer A: $75$

Employee Reject

Employee: $0$

Employer A: $0$

Employee Accept

Employee: $75$

Employer A: $90$

Employee Reject

Employee: $0$

Employer A: $0$

Assume this is a sequential game.

If employer A offers a low salary, you, as the employee, are best served by the offer. In this case, you would earn a payoff of $,$ and employer A would earn a payoff of $.$ Alternatively, if employer A offers a high salary, you are best served by the offer. In this case, you would earn a payoff of $,$ and employer A would earn a payoff of $.$ With this information, employer A will choose to make a offer, since it will yield a higher payoff for her, based on what you $($the employee$)$ will subsequently choose.

Suppose you have a competing job offer from employer B$.$ Accepting this job offer gives a payoff of $82\mathrm{.}5.$ During your negotiations with employee A$,$ you have the option of taking this offer from employer B$,$ and employer A is aware of this offer $($as well as the payoff to you$).$ Given this competing offer, the negotiation with employer A is depicted in the following figure:

Employer

High Offer

Low Offer

Employee Accept

Employee: $90$

Employer A: $75$

Employee Reject

Employee: $82\mathrm{.}5$

Employer A: $0$

Employee Accept

Employee: $75$

Employer A: $90$

Employee Reject

Employee: $82\mathrm{.}5$

Employer A: $0$

True or False: With this competing job offer, your threat to reject employer A$\text{'}$s offer, if it is low, is now credible.

False

True