Information Flows And Networks I

Predicting The Optimal Stopping Point

Note: in order to run the simulation referred to in this slide, go here, to the Java Applet version. You will be directed to download the latest version of the Java plug-in.

The manager in the previous slide was seemingly in the dark: she didn't quite know the optimal point at which to stop searching for a better job candidate. In fact, however, the probability distribution function of interviewee worth happens to be very valuable information, provided the manager can figure out how to use it. In other words, by knowing that each candidate's worth is equally likely to fall anywhere between 0 and 100, she can figure out the expected payoff (marginal reward minus the cost) of the next interview. When that value falls below zero, it's a sign that the blue line of the manager's Total Payoff is likely to start falling soon.

Accordingly, in the graphic to the left, we have reenacted the scenario from the previous slide, with the addition of a few measures that can help the manager decide whether to go on with the interviewing process. As mentioned above, when the graph's red line - expected payoff from the next interview - drops to zero, the manager is well-advised to stop interviewing altogether. Another useful measure one can surmise from the probability distribution is the expected number of interviews left until the optimal point is reached. Not too surprisingly, its value falls by an average of one with every time step, and drops to zero at the same time as the expected payoff of the next interview.

If you are curious as to the mathematical details of computing the expected interview payoff, go to the mathematical appendix at the end of the tutorial. Otherwise, go on to the next slide for another kind of optimal stopping simulation.