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?
Tim Harford gave a wonderfully clear answer that explains mixed strategy equilibrium in game theory. Harford concludes:
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.
Although Harford does not make this explicit, it's probably true that there are different types of people out there, each with a different level of nostalgia for holding the Michael Jackson memento. In this case (and with a smooth distribution of types of people), only one fan type will be willing to randomize. That's the fan who has the "right" level of nostalgia. And, that right level of nostalgia is determined by supply and demand.
One way to express this nostalgia is to ask each individual (independent of market conditions) what price would make him just indifferent between holding the ticket and selling it. This reservation price will probably differ across individuals, but it will convey the distribution of types. People with a reservation price of $0 are the non-nostalgic types, whereas people with very high reservation prices are the nostalgic types.
Now, let's return to Harford's example. Like Harford, let's suppose that 100,000 memento tickets* is the equilibrium quantity. In this case, who are the 100,000 people who accept the ticket instead of the refund? They're the ones with the highest reservation prices, or the lowest levels of nostalgia. No psychology or irrationality required.
That brings me to my poll question of the week:
What's your Michael Jackson ticket reservation price? (pick the closest number)
Please vote early and often. Tell your friends and fans to vote. The poll is open for a week. I look forward to seeing what you have to say.
*Note: Like Harford, I punted on completely spelling out the equilibrium conditions. Really, the marginal type has to be indifferent in equilibrium. One could express this indifference mathematically, but this is a blog.