You go into a restaurant and ask them the wait time for a table for two.  The hostess says 45 minutes.  Is she making it up off the top of her head?

I have always wondered about this.  It turns out that some restaurants have a more sophisticated approach.  They use software sold to them by opentable to estimate wait time.  There is one employee whose job it is to wander round going table to table eyeballing the state of the meal.  How many people are eating dessert?  Have they paid or are they waiting for the check?  This information and more is inputted into the software.  The software then churns out an estimated wait time by size of table. This much I know.

What I don’t know is whether the hostess then adds or subtracts a fudge factor as a function of wait time.  For example, if there is excess demand but the queue is short do you underestimate the wait time to encourage people to stay?  The paradigmic incentives in the Crawford-Sobel Cheap Talk model arise for the restaurant.