Solution to the game theory challenge

Let me say two things first.

This is an article about game theory.  It doesn’t constitute investment advice.

This article presents the solution to a game theory problem.  You should really take a look at the original problem before reading any further.  You can find it at http://sscactuaries.co.uk/a-game-theory-challenge/

Done that?  OK.  Here’s the solution.  Some of you will be amazed by its simplicity, others disappointed.

Let’s start off by thinking what would happen if you turned over the 12th and final picture card.  You’d have to pay someone else for a crisp bag and, with no more picture cards to come, you’d never get the chance to sell it on.  Remember that.

Now imagine the 11th picture card has just been revealed.  Someone else has just paid for the crisp bag and you’re thinking about whether to turn a card or to quit.  It’s a no brainer, isn’t it?  If you turn a picture card, you pay for a crisp packet that you can’t sell because there are no more picture cards left.  So that would lose you money.  And are there any opportunities to make profits by staying in the game?  No.  If carrying on gives opportunities to lose money but not to make money, you should leave the game.  A game theorist would say that the decision to quit dominates the decision to stay in.

Everybody around the table can work this out.  So when the 11th picture card is turned over, everybody quits and the guy drawing the 11th picture card has paid for a crisp packet that he can’t sell.  If someone draws the 11th picture card, they won’t be able to sell it on.  Remember that.

Now imagine the 10th picture card has just been revealed.  Someone else has just paid for the crisp bag and you’re thinking about whether to turn a card or to quit.  It’s a no brainer, isn’t it?  If you turn a picture card, you pay for a crisp packet that you can’t sell because we’ve already worked out that whoever draws the 11th picture card won’t be able to sell the crisp packet.  So that would lose you money.  And are there any opportunities to make profits by staying in the game?  No.  Again you should leave the game.

Everybody around the table can work this out.  So when the 10th picture card is turned over, everybody quits because they don’t want to draw the 11th.

And when the 9th picture card is drawn, everybody quits because they don’t want to draw the 10th.

Keep going like this and you’ll find that when the first picture card is drawn, everybody quits because they don’t want to draw the second.

And at the start of the game, everybody quits because they don’t want to draw the first picture card.

So there’s the answer.  According to game theory, the best strategy is to never turn a card over.  Quit as quickly as you can.

And this is all based on game theory.  In a room full of John Nashes, this is exactly how everybody would play.  Of course, in a room full of lesser mortals, there are alternative strategies that could make you money but that’s a different matter.

Please remember this does not constitute investment advice.

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