The Mathematics Behind Exploding Offers

Attracting top talent is among the most important — and most challenging — responsibilities of any manager.  Yet few steps in the hiring process are as poorly understood — and as fraught — as the timing of a job offer.

Should you make an offer on the spot?  Should you wait until you’ve interviewed others? How much time should you give a candidate to accept? Is it a good — or a terrible — idea to make an “exploding” offer, one with an unreasonably short deadline, in order to compel a quick decision?

All these questions and others were explored by Darden professor Saša Zorc and INSEAD professor Ilia Tsetlin in their latest research, forthcoming in the journal Operations Research. What they found, using game theory and mathematical modeling, is that only a handful of factors matter when it comes to an offer’s timing and its acceptance deadline.

Looking to Game Theory for Answers

Game theory, an established branch of economics now used across many fields, offers interesting ways to reason about so-called “two-agent systems,” in which one person’s (or agent's) decisions and behaviors depend on those of another. Using a game-theoretic approach, Zorc and Tsetlin developed a mathematical model in which two agents search for options to maximize their respective rewards, such as in a job offer setting.1

Typically, an employer is searching for the best candidate for a given role; the other agent, the job seeker, is looking for the best job that meets their needs and expectations. In Zorc and Tsetlin’s model, which approximates real life, the employer controls not only the offer’s value but also its timing and the amount of time the job seeker has to accept or reject it.

Job-Offer Timing and Deadlines: A Few Rules of Thumb

Zorc and Tsetlin found that the job seekers, after receiving offers with an extended deadline to respond, become more selective about accepting other offers, since they’re secure in the knowledge that they have an option to fall back on, should their search for a better alternative not pan out. In other words, the employers can effectively make the job seekers reluctant to accept other offers by giving them longer deadlines.

This reluctance, which Zorc and Tsetlin call the acceptance-deterrence effect, can be strong or weak depending on other factors. They discovered that the employer should choose between a short or a long deadline by knowing the strength of the acceptance-deterrence effect. An exploding offer makes more sense, they found, when the acceptance-deterrence effect is weak; when the effect is strong, the employer may benefit by giving the job seeker more time to consider the offer.

But just how can an employer find out the strength of the acceptance-deterrence effect? Zorc and Tsetlin found that knowing the answers to only two questions is sufficient:

• Is the employer likely to know when the job seeker receives another offer, and will the employer have an opportunity to respond to that other offer? If so, the acceptance-deterrence effect would be weak. The optimal strategy for the employer would be to wait until a suitable time and then make an exploding offer. (This scenario tends to be common in small markets, such as when universities hire new assistant professors.)
• Will the chances of the job seeker getting other offers, or the value of such offers, change over time? If they do, the acceptance-deterrence effect would be strong. Hence the employer can expect a better pay-off by giving the job seeker a longer deadline. (The MBA job market is an example. The probability and value of a student’s job offer change over time, since different industries start the recruitment process at different points of the recruitment season.)

Negative Behavioral Consequences

Zorc and Tsetlin have one important caveat for their findings: Their two-agent mathematical model does not include the social and behavioral factors that can affect people in these situations. For instance, there’s compelling evidence that exploding offers do not lead to productive, long-term relationships. Research has shown that employees tend to respond to such offers with unmotivated performance and short tenure in the job.

Taking this into account, Zorc and Tsetlin have some measured advice for employers: When a shortened deadline seems to be the optimal strategy, shorten it only to the extent that is socially acceptable — do not make the deadline any tighter if that would trigger negative psychological and behavioral effects in your prospective employee. The last thing any employer wants is to sour the relationship with a great, new hire. So, if you’re choosing to ignite an exploding offer, just make sure it doesn’t explode too much.

Saša Zorc co-authored “Deadlines, Offer Timing and the Search for Alternatives,” forthcoming in Operations Research, with Ilia Tsetlin of INSEAD.

• 1This two-agent setting occurs in a range of markets, such as venture capital, mergers and acquisitions, real estate and player transfers in sports. Here we focus on its application to job offers in order to illustrate the model and its insights.