Game theory and North Korea

Peace and WarKim Jong-Un is a new leader in a dangerous situation. Hopefully he’s read up on some game theory!

There are lots of ways to look at the North Korean situation through the lens of game theory and this post looks at what various commentators have been saying.

Evan Osnos has written in the New Yorker that Kim is a dangerous wildcard but that China will continue to support him because having him in charge is preferable to the Americans or South Koreans taking charge in North Korea.

Gregory Boyce thinks that this is a game of chicken where Kim is trying to responding to internal pressures from his military leaders.

Tyler Cowen looks at the situation from the American standpoint saying that they have to take the position they do in support of the South Koreans to give confidence to their other allies such as Israel. The Americans don’t really support South Korea that much but they use their support to send a message to others.

Don Rich also brings Israel into the analysis. He also raises the tricky problem of how Kim can keep the domestic support he gains from his aggressive stance if he then backs down. It is all made more difficult by cultural differences and the risk that Kim Jong-Un may not be acting rationally at all.

This brings me to the final article by Tim Worstall who says that in his experience of dealing with the North Koreans, including handing over £10,000 in cash to get a rail freight deal concluded, shows that they might just be crazier than anyone gives them credit for!

Having read these it is my view that China are the key to the situation. They support North Korea because they would not want to see the Americans occupy the land. It is this Chinese support that gives Kim the confidence to sabre-rattle so loudly without worrying about a US invasion, but equally they won’t want him to actually start a war which they would either have to get involved in or let him lose.

How do you think the game will play out?

Image courtesy of Stuart Miles / FreeDigitalPhotos.net

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St Petersburg paradox explanation

Undecided gamblerThis is an interesting example from decision theory (which is pretty closely linked to game theory).

A (very generous!) casino offers you a game where the pot starts at $1 and on each turn a (fair) coin is tossed. If it comes up heads then the pot is doubled, if it comes up tails then you win whatever is in the pot.

How much would you pay to play this game?

Half the time a tail comes up on the first coin toss and you win $1. Half the time you get a head, the pot doubles to $2, and you get to toss the coin again.

On the second toss, half the time you get a tail and win the $2 and half the time you get a head again and the pot doubles to $4 and you get to toss again.

Overall you get the following pattern. Half the time you win $1, a quarter of the time you win $2, one eighth of the time you win $4, etc. The amount you win gets bigger and bigger, but the chance of winning that amount gets smaller and smaller.

This means that you should expect to win:

(1/2 x $1) + (1/4 x $2) + (1/8 x $4) + (1/16 x $8) …

There are an infinite number of terms in this equation.

which is

50c + 50c + 50c …

which is the same as an infinite number of 50 cents, which is infinity.

So using an expected value argument you would pay an infinite amount to play the game because you will win an infinite amount.

However you almost certainly wouldn’t pay a massive amount to play the game. There have been a number of arguments put forward to explain this:

Daniel Bernoulli in 1738 was the first to attempt to resolve the paradox. He suggested that because each extra bit of money means less to you then you won’t value the later money you could win as much. Basically, if you have nothing then $1,000 is a lot of money, if you have $100 million then an extra $1,000 is irrelevant.

Another argument is that people don’t imagine that such a long string of heads is possible. Most people instinctively imagine that after a long run of heads a tail is more likely, even though it isn’t. That’s why casinos show all the recent numbers that have come up on a roulette table, because people are looking for patterns to base their next bet on.

One more argument is that the casino only has a limited amount of money and cannot payout an infinite amount. If the casino is willing to risk $1,000,000 on the bet then the expected payout drops dramatically. It takes a run of 20 heads to take the payout to over $1,000,000, this means that the expected payout drops to a bit over $10. The high expected value normally comes from having some incredibly rare but extraordinarily high payouts, without these the value drops substantially.

Which explanation do you prefer for the paradox, or do you have your own?

 

 

Image courtesy of marin / FreeDigitalPhotos.net

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Trapped by a prisoners dilemma

Royal Crescent Bath

Royal Crescent Bath

I am lucky to live in the beautiful city of Bath in the south-west of England. Bath is renowned for its Roman Baths and Georgian architecture but its council has fallen into a prisoners dilemma.

The city has three main recycling centres to encourage people to recycle as much waste as possible. At the moment anyone can use the centres whether they live in Bath or not. Equally anyone in Bath can also use a centre in another city if they want to. I sometimes use a centre in another area because it is on my way to work.

I don’t know how much they spend on the recycling service but let’s assume it is £100,000 (it’s always good to use a nice round number!).

If 10% of people come from other areas and they are banned from using the sites then the cost will fall to £90,000, but the council will now have to pay the cost of monitoring who is using the sites. Let’s say monitoring cost is £5,000, then the cost for the council becomes £95,000. The council has saved £5,000 by stopping people from other areas from using the service. The neighbouring council now has more people to deal with because no-one from their area can go to Bath anymore. Their cost goes up to £110,000.

This is fine for Bath until the neighbouring councils do the same thing. When that happens then the 10% of people who were going from Bath to another area (like me) can only use the Bath centres. This now adds £10,000 back onto the Bath cost bringing it up to £105,000. This is the original cost of the service plus the cost of monitoring who is using it.

Showing the game in a grid looks like this:

Accept others Residents only
Accept others (£100,000; £100,000) (£110,000; £95,000)
Residents only (£95,000; £110,000) (£105,000; £105,000)

We can see that this is a classic prisoners dilemma.

If the other council is accepting others then Bath is better off if it restricts its service to residents only (a cost of £95,000 rather than £100,000).

The alternative is that the other council limits its service and then Bath’s best response is also to limit its service (a cost of £105,000 rather than £110,000).

Either way the best response is to limit the service even though this leads to a worse result for both than if they both kept an open service.

That’s explains why they have decided to restrict the service to residents, but why has this only just started to happen when the service has been running for years?

The answer is because the councils have changed the game they are playing. Before the ‘Great Recession’ the councils based their service around maximising the amount of waste that is recycled. When this is their priority then they have no reason to restrict who uses the service, all that matters is that the waste is recycled.

Now the council’s are playing the game using money as the measure of success. This has changed the game into a prisoners dilemma and the councils are now trapped.

This is a real life example where changing what is important in the game has changed the outcome.

What you measure matters because it changes the game

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