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augusti 14, 2005

Spelteoretisk analys av uppvaktning

New Scientist: 'Worthless' gifts get the good girls berättar om två brittiska forskare, Peter Sozou och Robert Seymour, som gjort en spelteoretisk modell kring uppvaktning.

Från New Scientiskt-artikeln:

Men who spend big money wining and dining their dates are not frittering away hard-earned cash. According to a pair of UK researchers, they are merely employing the best strategy for getting the girl without being taken for granted.

Using mathematical modelling, Peter Sozou and Robert Seymour at University College London, UK, found that wooing girls with costly, but essentially worthless gifts – such as theatre tickets or expensive dinners out – is a winning courtship strategy for both sexes.

So [Sozou] and Seymour built a model based on a series of dating decisions. In the model males had to decide what kind of gift to offer females – valuable, extravagant or cheap – based on how attractive he finds her. The females had to either accept or decline the gift and then decide whether to mate with the gift-giver – a decision also weighted on the 'attractiveness' of their prospective partner.

When they measured the different outcomes of all the steps, they found the best solution for the males was to give extravagant, but intrinsically value-free gifts the vast majority of the time, while giving gifts of material value very occasionally.

The model showed that if males gave valuable gifts too often, the females would start to exploit them: the males have no clue as to the females’ real intentions in the model. Put simply, the females just take the diamonds and run. But when the gifts are worthless, an uninterested female has little incentive to accept, gaining no return on what could be just turn into the simple waste of an evening. Only girls who are serious would bother to go the distance.

Naturligtvis har modellen inte fått stå oemotsagd:

Alison Lenton, a social psychologist at the University of Edinburgh, UK, questions some of the model’s assumptions, however. For example, one assumption is that females obtain a negative outcome for accepting an unattractive, though committed, male. Women have been shown to prioritise traits associated with good parental care above physical attractiveness, she says.

Matematikern Keith Devlin intervjuas i en NPR-intervju om detta: Using Math to Move a Courtship Forward. (Det kommer först några sekunders reklam innan programmet.)

Papret
Papret är alltså Peter D. Sozou, Robert M. Seymour: Costly but worthless gifts facilitate courtship.
Abstract:

What are the characteristics of a good courtship gift?We address this question by modelling courtship as a sequential game. This is structured as follows: the male offers a gift to a female; after observing the gift, the female decides whether or not to accept it; she then chooses whether or not to mate with the male. In one version of the game, based on human courtship, the female is uncertain about whether the male intends to stay or desert after mating. In a second version, there is no paternal care but the female is uncertain about the male’s quality. The two versions of the game are shown to be mathematically equivalent.We find robust equilibrium solutions in which mating is predominantly facilitated by an ‘extravagant’ gift which is costly to the male but intrinsically worthless to the female. By being costly to the male, the gift acts as a credible signal of his intentions or quality. At the same time, its lack of intrinsic value to the female serves to deter a ‘gold-digger’, who has no intention of mating with the male, from accepting the gift. In this way, an economically inefficient gift enables mutually suitable partners to be matched.

Det finns även appendix som mer förklarar modellen.

Not: Thomas på 1 är inte ett stort tal skrev om detta för ett tag sedan, i I brist på annat.

Mer om matematik och romantik
Om man vill vet lite mer om romantikens matematiska vedermödor är t.ex. J. C. Sprotts Dynamical Models of Happiness (PDF) ett bra ställe att börja läsa. Där beskrivs olika typer av personligheters dynamik med hjälp av differentialekvationer (och inte spelteori som Sozou och Seymours modell). Notera att papret är mer om dynamiska system än seriös romantisk forskning. Inspirationen kom från Steven Strogats lilla Love Affairs and Differential Equations (hittar den inte på nätet längre), och Strogatz skriver även om detta i sin bok Nonlinear Dynamics and Chaos. Eller söka på "differential equations" "romeo and juliet". Ett mer seriöst paper i samma anda är Sergio Rinaldi: Laura and Petrarch: An Intriguing Case of Cyclical Love Dynamics

I Devlins NPR-intervju nämns också Gottman, Murray et.al Mathematics Of Marriage (c.f. här, här och lite här.)

Se även Devlins populärmatematiska krönikor Devil's Angle).

Posted by hakank at augusti 14, 2005 10:30 FM Posted to Spelteori och ekonomi

Comments

Posted by: thebe at augusti 19, 2005 12:13 FM