## Using game theory for salary negotiation

Negotiation is often associated with the notion of being an art but along the course of this article, the logical and analytical components of negotiation are brought to the forefront. Although the arguments stated in this article can be applied to negotiation in most situations, in the interest of better explaining and articulating the insights gained from applying game theory to negotiations the specific example of salary negotiation is used.

Lydia Frank, the editorial director for compensation website payscale.com says, “If you don’t advocate for yourself, no one is going to do it for you.” Additionally, the author of the article referenced below says, “Salary negotiation is a game, and the first to give a number loses.” Taking into consideration, the both of these opinions, it can be said that the best possible strategy would be to certainly negotiate with your (the applicant’s) recruiter, but only after he/she gives you a number first. We will use game theory to prove this below.

Every situation is unique and depends on various other factors such as the size of company, relationship with the recruiting manager, and the stage in the recruiting process that an applicant is in. But we can generalize these situations by considering only the aspects of who gives a number first and what their stance is. Such a generalized form can be simulated by conducting a game, where the applicant and the company’s recruiter both write their salary expectations on separate cards, and then each player flips his/her card over one at a time. But to simulate the situation of which player “gives a number” first, the game involves the second person getting to change his/her vote after the first move. All the possible outcomes in the case of the recruiter getting to change his/her stance after seeing the applicant’s stance (this simulates an example where the applicant gives a number first) are given below:

Company’s Expectations |
|||

Low |
High |
||

Applicant’s Expectations |
Low |
Job, 🙁 |
Job, 🙁 |

High |
No Job, 🙁 |
Job, 🙂 |

In the above game, both the cases in which the applicant expects a low salary result in the applicant acquiring a job but being disappointed due to the low salary. This is because even if the recruiter has high expectations, in this game, the recruiter will change his/her stance after seeing that the applicant has lower salary expectations. Also, if the applicant were to have high expectations, the applicant would either not get the job (in the case of the company having low expectations, as the company isn’t willing to pay the applicant as much as he/she expects) or get the job with a high salary as desired (in the case of the company’s expectations matching with those of the applicant).

The applicant only gets the high salary **25%** of the time, and in one unfortunate case (No Job, 🙁 ), he/she is asking for much more than the recruiter intends to offer.

Now if we consider all the possible outcomes in the case of the applicant getting to change his/her stance after seeing the applicant’s stance (this simulates an example where the recruiter gives a number first) given below:

Applicant’s Expectations |
|||

Low |
High |
||

Company’s Expectations |
Low |
Job, 🙁 |
Job, 🙁 |

High |
Job, 🙂 |
Job, 🙂 |

In the above game, both the cases in which the applicant expects a low salary result in the applicant acquiring a job but being disappointed due to the low salary. This is because even if the applicant has high expectations, in this game, the applicant will change his/her stance after seeing that the recruiter has lower salary expectations, so as to secure the job. Also, if the recruiter were to have high expectations, the applicant would always get the job with a high salary because, if he/she initially had a lower expectation then after seeing the recruiter’s expectation he/she would higher his/her own expectation and if the applicant were to have high expectations as well then it would be a perfect match.

When the company is the first to give a number, you always get the job, and you have a **50%** chance of getting a high salary.

Therefore, from what we observe in the two game scenarios above, we learn that when the company is the first to give a number, the applicant has twice the chance of getting the job with a high salary. This can be generalized to any negotiation in that the first party to express their stance usually stands at a disadvantage.

Reference article: http://stevehanov.ca/blog/index.php?id=67

Note: Getting what is expected in the case of a “low salary expectation” results in a “L,” according to an example that was given by the author of the referenced article but can also be looked upon positively, as the applicant is receiving what he expected. Here, we will work by assuming/considering a low salary to be a disappointing outcome.