So, if you haven’t already, you’ll probably soon receive the credit card bill with all of your Christmas purchases on it. Was it worth it? Well, was it, punk?

If you’re like most people, some of your presents were probably intended to impress someone. The question is, what’s the best kind of present for that? Should I give the girl from math class diamond earrings, or new batteries for her calculator? Should I give my boss a mug, or a gift certificate to Glamour Shots?

Fortunately, Science!™ has the answer. Today’s journal club entry concerns a model of gift-giving that considers three different types of gift that differ in their cost to the giver and their value to the recipient. “Cheap” gifts are, well, cheap. “Valuable” gifts are expensive to give, and have value to the recipient. The interesting category is the third one, the “extravagant” gifts, which are expensive to give, but have little inherent value to the recipient.

The specific context is gift-giving and mating. The model is of a sequential game with three or four stages. First, the male offers a gift to the female. Second, the female either accepts or rejects the gift. Third, she chooses whether or not to mate with the male. Then, in one version of the game, the male decides whether or not to stick around and contribute to the care of the offspring.

This $305 luxury frisbee is an example of an extravagant gift.

The conclusion of the paper is that there are many combinations of parameter values that will lead to males giving extravagant gifts. There are two critical features of the model that seem to be necessary in order to get this result.

First, there is uncertainty. The female has a guess about the quality of the male (or, equivalently, in the version of the model with paternal care, the probability that he will stick around after mating). By accepting the gift, she gains additional information about his quality or intentions. Similarly, the male is uncertain about the quality and intentions of the female – whether it is worth it for him to stick around after mating, and whether or not she is a gold-digger, who will just take his gift and skip town with his cousin.

[Editorial note: the term “gold-digger” is from the paper. Those of you who know me know me know that I would never have gone with such a politically incorrect term. I would have used “■■■■■■■■■■”.]

[[Meta-editorial note: parts of the previous editorial note have been redacted.]]

The other key feature is that there must be some cost to the female in accepting the gift.

Now, there are lots of parameters in a model like this, and several equilibrium solutions are possible. The interesting one is the one where males give cheap gifts to unattractive females (females whom they judge, with some uncertainty, to be of low quality), and give extravagant gifts to attractive females.

The key to getting the interesting equilibrium is that the ability or willingness to provide and extravagant gift has to correlate with the male’s quality or intentions. For example, a male can’t afford to spend two-months salary on a diamond ring every time he wants to have a one-night stand. Therefore, an extravagant engagement ring becomes a reliable indicator of his intentions. Ideally, the gift has to have no inherent value to the female, for example, if it were impossible to sell the engagement ring for cash money. Recall also that it has to cost her something to accept the gift. Then, taking the gift constitutes a commitment on her part as well. Otherwise, she benefits most from accepting the gift and walking away.

In the salacious application-to-human-mating case, this cost to the female is easiest to envision as a reputation cost (e.g., the risk of being labeled as a ■■■■■■■■■■). In certain species, where females mate with multiple males, store the sperm, and then use it selectively, there may be direct opportunity costs that do not require catty moralizing.

Just one last point.

The paper starts with, “Gift-giving is a feature of human courtship”. The authors cite Geoffrey Miller’s 2000 book, The Mating Mind. If the paper were being written today, I assume they would have cited more recent work by Hefner and Harris.

Sozou, P., & Seymour, R. (2005). Costly but worthless gifts facilitate courtship Proceedings of the Royal Society B: Biological Sciences, 272 (1575), 1877-1884 DOI: 10.1098/rspb.2005.3152