# Cash or Ticket?

I’ve been a boyhood fan of Michael Jackson, and so will not comment on his life or death out of respect – other than to say he was an inspirational artist in many ways.

However, the situation with his concert tickets caught my eye as an interesting application of game theory. Just to set the scene, MJ had planned a series of concerts at the O2 Arena in London. 50 days were promised, and with a capacity of around 20,000, this implies that around a million tickets would have been sold for the shows in total.

As we know, Michael sadly died before any of these concerts took place. For the promoter AEG Live, this meant that they had to offer full refunds to everybody who bought a ticket. Interestingly, they also offered these people the option to forego their refund for a printed version of the ticket they would have received prior to the show they were attending. This way, AEG could avoid having to pay everyone back, as there would undoubtedly be people who would rather have the memorabilia than the money.

##### The Decision

I’m going to try to build a (very) simple model to help me decide what I would do if I was a ticket holder.

The ticket price would have varied depending on where one bought them from, and the location of the seat. I’m going to assume an estimate of £100 as the average ticket price, and so this would be the amount that I would get if I claimed the refund.

I’m also going to make the assumption that if only one person claimed the ticket, it would be worth £100,000.

Obviously, a refund would guarantee my £100 back, no matter what anyone else did. If I was the only one who claimed a ticket, then I would get the full £100,000 resale value, since it would be the only one in existence.

However, the interesting phenomenon arises when we have to consider how many other people claim for their tickets – i.e. the value of x. Suppose I get 100,000/x if I claim the ticket, and there are x people who claim the ticket in total.

• If x>1000, then I’d rather get a refund, as the ticket would then be worth less than £100.
• If x<1000, then I’d claim my ticket, as it would be worth more than £100.
• If x=1000, then I’d be indifferent between doing either, as I’d get £100 either way.

There is a lot of room for exploration here, because the game would require probabilities (I don’t know what x would be, and so I would have to base it on some sort of expectation). The model could get quite complicated if we considered all possibilities and started using probabilities (which, quite frankly, would give me nightmares).

##### Guesstimation

Suppose I expect that 5% of people decide to claim their ticket – this seems like a sensible proportion to conjecture. This would still be 5000 people, hence I’d be much better off getting a refund. Based on this, it seems sensible that if I had bought a concert ticket – I would not claim my ticket and instead get a refund.

If everyone thought that this would happen, then it would be in my interest to break the pattern and claim the only ticket whilst everyone else got their refund. However, everyone else thinking this would follow suit, and so there seems to be no clear equilibrium here in a pure strategy.

Of course, in reality, one’s decision to claim a ticket would be more emotional than rational, and so a formal model would probably not apply. It would, however, be interesting to expand on this to find a formal mathematical solution in future…