Michael Jackson: ticket or refund?
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?
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.
Also published at ft.com.