Can game theory help you negotiate your salary?
Link: https://williamspaniel.com/2014/09/28/what-does-game-theory-say-about-negotiating-a-pay-raise/
What can an employee do to maximize her chances of negotiating a higher salary? According to William Spaniel, the author of the linked article, one of the most important tactics is to “not be afraid to reject offers and make counteroffers.” To see why Spaniel’s advice is correct, imagine if only the employer was able to make an offer, and the employee could only accept or reject. Spaniel notes younger employees of often inadvertently put themselves into this situation, especially at the time of hire. Too often, he says, “a hiring manager might propose a wage. The new employee, deathly afraid of losing the position, meekly accepts”. Spaniel then mentions that this gives all of the bargaining power to the company, leaving no room for the employee to better her situation.
You probably already had a hunch that the employer has the upper hand, but game theory can prove this fact rigorously. Let’s say the employee values herself at $60000 a year, while the company values her at $50000 per year. This leave a difference of $10000 that remains to be negotiated. The company, as the only party able to make a proposal, is now essentially deciding how much of this $10000 it ought to give the employee, and how much to keep for itself. For example, the company could decide to be fair and give the employee $5000 and keep $5000 for itself, meaning that the negotiated salary would be $55000.
Let’s consider the employee’s strategy in this game. If the employer offers her some amount x, she can accept the deal and receive a payoff of x. In this case, the employer would receive a payoff of $10000 – x. However, if the employee rejects the offer, then both players would receive a payoff of zero, as no deal was formed. We now consider two cases: when x = 0 and when x >0. We summarize this scenario with a payoff matrix:
Let’s assume the employee is going to accept any deal. Then the employer’s best response is to offer $0, leading to a payoff of $10000. Now let’s assume the employee is going to decline the deal. Then offering x > 0 and offering x = 0 are both best responses. This means that the employee has a dominant strategy of offering $0 to the employee.
This is bad news for the employee! Game theory has shown that the employer has no incentive to bargain with her at all if she cannot make a counteroffer. And even if the employer gave some amount x > 0 to the employee, making the employee’s best strategy to accept the offer, x could be a tiny fraction of the salary. Therefore, from a game theory perspective, it is crucial that the employee is willing and able to reject and make counteroffers to the employer’s offers, which is often the case in real life. With counteroffers, the game becomes much more fair, and is called Rubinstein bargaining. In fact, given an infinite number of counter-offers on both sides, infinitely patient players, and ignoring the costs of delays, the employee would be able to negotiate a salary halfway in-between the employer’s offer and her expectations.