Author | George G. Spyro
Translate | Guo Tingwei
Source | Mathematical Miscellaneous: Anecdotes in the Mathematical World
◆ Summary: What gifts should I buy for my loved ones? This romantic-sounding problem is actually just a simple decision-making problem that can be solved with boring mathematics. Scientists have found that using game theory and mathematical models, it is possible to find the best gift-giving strategy.
There is a young man who is in a dilemma, what gift should he buy for his beloved? How is he going to prove to her that he is serious about the relationship? Wealthy people who love to show off will choose expensive gifts to win hearts, such as diamond necklaces. Stingy will only send a custom jewelry. Sleek playboys will choose flashy things like a pot of orchids or premiere tickets at the Metropolitan Opera. This romantic-sounding problem is actually just a simple decision-making problem that can be solved with boring mathematics.
Peter Sozou and Robert Seymour of University College London are studying this question. They used game theory and mathematical models to find the best gift-giving strategies, which they published in the Proceedings of the Royal Society in 2005.
The model built by Sozhou and Seymour is a courtship game based on a series of dating decisions. The type of gift a man gives to a woman is a symbol of his status. The game begins with the man choosing a gift, what kind of gift he gives to the woman, expensive, flashy or cheap, depending on how attractive he finds the woman. Once the man has given the gift, the woman must decide whether to accept it, meet him alone, make love, and then the ball is in the man's hands, and now he must decide whether to associate with the woman or give up and find a more suitable person.
Both sides must be careful. On the one hand, the lady cannot immediately see the value of the gift, and only after receiving the gift can she judge its value. On the other hand, diamond rings are easy to liquidate, which in turn can make men hesitate. Both sides must adjust themselves according to game theory and probability, according to the possible intentions of the other. The man asks himself if the lady really likes him or is only interested in gifts; The lady wondered if the suitor was serious about being affectionate or if she only wanted a short encounter.
Soph and Seymour need to find out what constitutes the so-called Nash equilibrium, named after the mathematician and Nobel laureate John Nash (May 23, 2015, john Nash and his wife died in a car accident in New Jersey, USA, at the age of 86, and the movie "A Beautiful Mind" has become familiar to non-mathematicians. If neither men nor women can benefit from unilaterally changing their strategies, this state is in equilibrium, and nash equilibrium points can be calculated, but the participants in the above game certainly do not do any calculations, and they find that the way to lead nash equilibrium is either through the pressure of natural selection or through the learning process (e.g. young people adapting to social customs). Once participants reach such equilibrium, neither side will be motivated to change strategy. This situation is asymptotic stabilization.
The two researchers found a total of 5 nash equilibriums. For example, the fifth case is as follows: "Men give cheap gifts to unattractive women, and expensive or flashy gifts to attractive women, both of which have a certain probability." Women accept all gifts from attractive men. If they later find out that the gift is worth a lot, they will decide to associate. "However, the most successful strategy for men is to give gifts that are high-priced but cannot be monetized by potential partners. Through this gift, the woman receives a double message: first, the man who pursues her is financially strong; second, he has a high opinion of her. At the same time, men can avoid selfish women who specialize in fishing kaizi, because gifts don't actually have real market value.
Incidentally, flashy gifts are not the preserve of humans, and animals prefer to give them. For example, when a male peacock tries to show off its feathered tail and engages in this ineffective but stressful behavior, the female peacock is quite obsessed with it. An unpleasant example, however, is the Australian mosquito scorpion, where the male manages to steal back its gift, a juicy insect, after mating, in order to give it to another female.
- Author -
George G. Szpiro, a journalist who turned from mathematician, master of mathematics at ETH Zurich, master of management from Stanford University, ph.D. in mathematical economics from the Hebrew University, taught at the Hebrew University, the University of Zurich, etc., and served as the correspondent of the Swiss newspaper Neue Zurich in Israel. He is the author of "Kepler's Conjecture" and "The Secret Life of Numbers". This article is an unauthorized excerpt from "Mathematical Miscellaneous: Anecdotes and Anecdotes in the Mathematical World", Shanghai Science and Technology Education Publishing House, if there is any infringement, please contact to delete.
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