Thursday, April 12, 2007

Game Theory and Justice

We've gotten a couple of comments on the tipping question. So here's a bit of elaboration. Game theory is simply a mathematical process of organizing situations of conflict and cooperation. Technically, game theory allows any preferences, but as a practical matter it has historically assumed that the game players (coaches, admirals, or consumers) were selfish. What game theory is very good at is tracking equilibrium notions of interacting incentives. Thus, in a standard game theory model, someone leaves a tip to insure better service from the same server in the future, or to improve his business prospects by impressing other diners, and so forth. The assumptions of the original example in "Who had the Roast Beef?" set up a paradox in which it seemed that there was no game-theoretic reason to leave a tip.

Recently, some game theorists have become interested in dropping the assumption of selfishness. This research has focused on altruism (roughly, I enjoy making other people better off) and preferences for equality of outcomes. For a number of complicated reasons, I am not a fan of these models. Instead, not surprisingly, I believe that the better concept is one of "doing the right thing" or biblically, "justice." Hence I asked the second question, "Why wouldn't you leave a tip?"

Once we recognize that the de facto American standard is that diners are paying part of a server's wages, then not to leave a tip is to deny a worker his wages, something explicitly prohibited throughout the Old Testament. To see my point, consider all of the people with whom we interact, many of whom earn less than the server, but for whom we do not leave a tip. The difference cannot be explained by altruism or equality. It may not make sense that we live in a social equilibrium in which the expectation is that customers pay part of a server's wages, but that expectation does not hold for servers in a party of 8 or more with a fixed gratuity, or for checkers at Best Buy, or for diners at restaurants in Europe. But it seems to me to be there.

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