Truck and Barter

But then I have an incentive to come even later, because I know you'll be late, and if I'm not as late as you, I'll still have to wait.

So a social agreement to be punctual seems to me to be optimal.

Only if the contract is enforceable. The contract would have to have some sort of punishment component, otherwise it's just an agreement with no force. The loss of reputation (that Chamberlain does mention)for being late would be one attempt at making the contract enforceable. But you'd have to show that the loss of reputation is somehow more of a loss than the time spent waiting. That is, my being 10 minutes late and wasting no time waiting for you would have to cost me less in terms of your (or the group's) opinion of me than being ten minutes early and simply sitting around.

A fuller model would also include concern for reputation that comes with being too early. That is, in a goodly number of professional settings the ability to be early to anything is often read by others as your having "not enough to do". Those who show up early were, in this view, clearly not fully employed in some important endeavor. Now, those who are late (again in this particular view) are seen by the rest of the group as more important, since something kept them busy right up until the time they left for your meeting. This belief of mine seems well supported by the number of times that an individual's being late to a meeting is accompanied by an explanation that includes some form of "I was on the phone/in another meeting/finalizing a report for the VP/Chairman/editorial board publishing my latest paper/Secretary of the..." and so on.

I have a doubt: Will the analysis hold if people try to be late deliberately?

Ashish-

I think I take your meaning. In the case that everyone who is meeting for lunch understands the implications, I suppose there might be a chance that things begin to unravel in an effect similar to the reasoning behind why immediate defection results in so many coordination games: if we cooperate for the average payoff for t times, I can profitably defect at the last period to get the higher payoff in that turn and increase my total payoff overall. Since you realize this as well, you beat me to the punch one period before, and so on down the line. Perhaps if I realize you're going to run late in order to avoid wasted time waiting, I'll be late for the same reason, allowing even more time than perhpas the 10 minute window Chamberlain talks about (I know you plan to be 5 minutes on the late side, so I choose to be about 6 minutes late, making me not have to wait at all). You know this, and thus choose to be 7 mintes late, and so on.

I think the question becomes: would we ever go to lunch?

I have a Tee time. Nobody is late!