【英语生活】要纪念门票，还是要退款？

Having just read the chapter on game theory in your book, The Undercover Economist, I discovered that Michael Jackson fans (circa 800,000 of them) are being offered the chance to receive their concert tickets as a memento, in place of a refund. I presume the future value of any one ticket will depend almost exclusively on the choices of the other 799,999 fans. To the non-nostalgic fan, who wishes only to see the best financial outcome, what would be your advice based on a game theory analysis?
Patrick Hudson

Dear Patrick,

I think it is safe to assume that if 799,999 fans take the memento ticket, the remaining fan would be better off taking the refund, while if 799,999 fans take the refund and one fan takes the ticket, the ticket will be very valuable. (We must also assume that the concert promoters will not then flood the market with the other 799,999 unwanted tickets.)

From a game theorist's perspective, the equilibrium solution is clear. Let us say that memento and refund are equally valuable if 100,000 take the memento and 700,000 take the refund. In that case, each fan should independently adopt a “mixed strategy” with a one-eighth probability of taking the memento. (A nerdy hint: roll three dice; there is a one in eight chance that the total is exactly 10.) Every fan will be happy to randomise, because every fan will know that either way, he or she will get something of equivalent value.

I realise all this sounds implausible, and it is. Game theory makes demanding assumptions about human rationality that may not apply to grieving fans. I would pay closer attention to research in economic psychology that suggests people are very unwilling to part with an item once they feel a sense of ownership. A non-nostalgic fan should go for the refund.
 

刚看完你在《卧底经济学家》(The Undercover Economist)一书中所写的有关博弈论的章节，我就发现，迈克尔•杰克逊(Michael Jackson)的歌迷们有机会获得作为纪念品的演唱会门票，来代退款。我认为，任何一张门票的未来价值几乎完全取决于其他799999位歌迷的选择。对于一个并不怀旧、只希望看到最佳财务结果的歌迷，按照博弈论的分析，你会给出什么样的建议？

帕特里特•哈德森(Patrick Hudson)

亲爱的帕特里特：

我认为可以大胆假设，如果799999位歌迷都选择纪念门票，那么剩下的那位歌迷最好是选择退款；而如果有799999位歌迷选择退款、只有1位歌迷选择门票的话，那么这张门票将非常珍贵。（我们还必须假设，演唱会主办方此后不会用剩余的799999张无人选择的门票冲击市场）。

从一个博弈论者的角度看，均衡解是显而易见的。让我们假设，如果有10万人选择纪念门票，70万人选择退款，那么纪念门票和退票的价值是相等的。在这种情况下，每位歌迷都应独自采取有八分之一几率获得纪念门票的“混合策略”。（一个有些学术性的提示是，掷三个骰子，有八分之一的几率正好掷出10。）每位歌迷都会乐于随机选择，因为每位歌迷都知道，无论选择哪个，他或她都会获得同等价值的东西。

我明白，这一切听起来令人难以置信，确实是这样。博弈论严格假设人是理性的，这一点或许不适用于悲伤的歌迷们。我愿更密切的关注经济心理学方面的研究。这一研究表明，一旦人们对某样东西产生拥有感，他们就非常不愿意放弃它。一个不怀旧的歌迷应该选择退款。

译者/君悦