Anglo Irish bondholders face dilemma

From the FT

In the classic game theory case of the prisoner’s dilemma, two parties can either co-operate for some mutual gain, or each can sell out the other in the hope of a higher individual reward – but with the risk of losing everything if the other beats them to it.

This is the choice facing Anglo Irish junior bondholders when they vote this Friday on an exchange offer that, if approved, would see them receive just 20 per cent of the face value of their bonds.

Bondholders could work together to vote down the deal and force the bank to the negotiating table in the hope of a better offer – just as two theoretical prisoners who each stick to their agreed cover story can ensure neither is found to have committed the crime.

Read the whole thing.

Tit-for-Tat

Tit-for-tat is one the simplest strategies when faced with a prisoner’s dilemma type situation.  The only simpler strategies would be the pure strategies of “always cooperate” and “always defect”.  Neither of these will be very successful.

Tit-for-tat has a simple basic concept.

A player using this strategy will initially cooperate, then respond in kind to an opponent's previous action. If the opponent previously was cooperative, the player is cooperative. If not, the agent is not.

The strategy was entered by Anatol Rappoport in the Robert Axelrod’s Tournaments and was the simplest and shortest strategy entered each time.  The interesting thing was that the strategy of tit-for-tat can do no better than tie with an opponent if used in an iterated prisoner’s dilemma.  Tit-for-tat never used an unprovoked defect to try and catch out an opponents.  Tit-for-tat is nice – never the first to defect.

Using the example of goals scored in football league, tit-for-tat is a strategy that results in games that are 5-5 draws, 5-4 losses or at worst a 5-3 defeat against all opponents. Tit-for-tat beats nobody but is involved in lots of high-scoring games. Strategies that are ‘not nice’ win most games 2-1 or draw 1-1. Strategies that ‘not nice’ never get beaten but are involved in lower scoring games.

In a sport league points are accumulated by winning individual games.  If the competition is about beating your opponent in each game then ‘not nice’ strategies will come out on top in the tournament. In life, business and most everyday settings the objective is not to beat your opponent but to be as well off as possible.  This generally involved maximising the utility, profits or well-being earned.

If there was a sport league with the objective to have the highest number of goals a ‘nice’ strategy such as tit-for-tat is far better. Tit-for-tat might never beat anyone but even in defeat it earns more than ‘not nice’ strategies do in victory, if payoffs are counted in goals.  Clearly, payoffs based on aggregate goals scored are not used to determine winners in football leagues, but in general life our well-being is defined by total payoffs than total wins. 

Thus at the aggregate level tit-for-tat wins because the aggregate sum of the payoffs earned are greater.  In the context of the Prisoner’s Dilemma tit-for-tat is involved in games with more cooperation so both players benefit from the mutual cooperation.

Here is a comparison of the performance of Tit-for-Tat and the entry by Nobel Prize winner Gordon Tullock in the first round of Axelrod’s tournament.

OPEC’s dilemma

The world's most visible cartel, the Organisation for Petroleum Exporting Countries (OPEC) announced last year that it was cutting output.  This report suggests that:

The group agreed to a record 4.2 million barrel a day cut in production in late 2008 as global demand fell 0.6 percent, the first decline since 1983. Members are now adhering to about 54 percent of that cut, the IEA’s monthly report showed. Compliance reached a peak of 79 percent in March 2009, based on Bloomberg data.

Since then the price of oil has fallen slightly and OPEC members are concerned about the value of the US dollar, in which their oil is priced.

The declining price of oil is probably as a result of two factors. Firstly, as the output cut was expected it is likely that markets had it priced in long before the meeting. Secondly, the price is all markets is as a result of the interaction of supply and demand. OPEC may be able to control supply but demand is not so malleable.

Of course, as James Surowiekci tells us here the problem with cartels is that individual members have the incentive to cheat. With the current fall in the price of oil, countries may actually want to increase output in order to maintain their oil revenues.

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On a related note we can consider the impact of lower oil prices. This can be considered in the same vein as Landsburg's discussion of the impact of recycling on the number of trees and the impact of a pesticide bans and cancer rates. Time Magazine asks Is Cheaper Oil A Good Thing?

Nice guys finish first

This follows on from our discussion of the Prisoner's Dilemma. When does it pay to cooperate and when does it pay to defect. Will mutual cooperation ever occur when it is in the collective interest to do so but individually each person has the incentive to defect?

Richard Dawkins wrote a book published in 1976 called The Selfish Gene arguing that natural selection and evolution means that self-interested genes dominate and lead to the extinction of more altruistic genes.

In 1984 Robert Axelrod produced a book called The Evolution of Cooperation. In it he argued that the possibility of continued interaction meant that mutual cooperation was possible as one must consider the shadow of the future, i.e. a defection now will lead to a punishment defection from the other player in future periods. In the iterated prisoner's dilemma both player would be better if they cooperated now and into the future.

In the second edition of The Selfish Gene published in 1989 Dawkins included a chapter based on Axelrod's work. He had also made a TV documentary of the material broadcast in 1987. Here is the 46 minute documentary. It's not as flash as Jasper Carrot!

Some more links on the Prisoner’s Dilemma

The Dollar Dilemma

A little bit of macro. The dollar is the reserve currency of the world. However as the US has been running huge trade deficits over the last decade or so central banks around the world, and particular in Asia, have been accumulating huge dollar reserves. These countries sell huge quantities of goods to the US and are paid in dollars. It is in each countries individual interest to diversify into other currencies by selling dollars. However, if all countries were to do this the value of the dollar would collapse as would the worth of their remaining dollar reserves. The lengthy post linked above looks at the role of this dilemma in the current financial crises. The actual dilemma is explained more succinctly in this letter to the Financial Times.

The Dating Game

This anecdote is a variation of the scene from A Beautiful Mind but is even more un PC. I offer it for information purposes only but the comment at the end of the post is an interesting take on it.

Quotes from the trenches

The 'Live and Let Live' phenomenon developed most readily where the fighting was sporadic, and where the proximity of the trenches allowed the men to see, hear and smell each other on a regular basis and slowly begin to lose their fear.

At the end of the day, one's own survival could best be guaranteed by not antagonising the enemy. Troops on both sides quickly appreciated this:

'It would be child's play to shell the road behind the enemy's trenches, crowded as it was with ration wagons and water carts, into a bloodstained wilderness... but on the whole there is silence. After all, if you prevent your enemy from getting his rations, his remedy is simple: he will prevent you from drawing yours.'

John H. Beith, a British officer

In some places, highly unusual friendships developed:

'One day, while our infantry was cooking, there was a shout from the enemy trench: could he come and eat too? He was invited over. The Frenchman came and ate and made himself comfortable. And from then on, whenever the Frenchman noticed that food was ready in the German trenches, he came and joined in.'

August Bader

Soldiers also cooperated across the lines to frustrate their officers' intentions:

'We received the following message, tied to a stone, from the German trenches opposite: 'We are going to send a 40-pounder. We have been ordered to do this, but we don't want to. It will come this evening, and we will blow a whistle first to warn you so that you have time to take cover.' All happened as they said it would.'

Regimental War Diary, the Fifth Leicestershire

'Live and Let Live' wasn't universally observed. It tended to break down where Tommies faced Prussians, where Germans faced Highlanders, or where élite regiments faced each other. It also became more difficult to sustain in the latter stages of the war as soldiers on both sides lost increasing numbers of friends:

'Speaking for my companions and myself, I can categorically state that we were in no mood for any joviality with Jerry. We hated his guts. We were bent on his destruction at each and every opportunity. Our greatest wish was to be granted an enemy target worthy of our Vickers machine-gun.'

Corporal George Coppard - With a Machine-Gun to Cambrai

However, 'Live and Let Live' was sufficiently widespread for officers to feel uneasy and threatened by its existence. In 1916, the British High Command issued a directive that was designed to counter complacency and promote a more belligerent spirit:

'With trench warfare, there is an insidious tendency to lapse into a passive and lethargic attitude against which officers of all ranks have to be on their guard, and the fostering of the offensive spirit ... calls for incessant attention,'

'The Offensive Spirit in Trench Warfare' - British Training Manual, March 1916

Raiding parties and snipers were seen as the best way to promote mutual hatred.Senior officers started appearing in the lines to demand greater activity:

'Higher ranks began to appear in our midst, chief of all... the brigadier general... followed by an almost equally menacing staff captain. What was my name? Why had I not organised raids? Visited the enemy's wire? I was to go!'

Lieutenant Edmund Blunden

Ordinary soldiers would often go to great lengths to protect themselves. They ventured out into no-man's-land and their officers wrote glowing reports describing their heroism. However, back at headquarters, some officers smelled a rat:

'It became increasingly difficult, as time went on, to obtain correct reports from officers' patrols... it was my habit to order samples of German wire to be cut and brought back... Thus one would know that the German line had been visited.'

Brigadier General Frank Crozier

Faced with such demands, some soldiers were still clever enough to outwit their superiors. One group of British soldiers found a coil of German wire in no-man's-land, lugged it back to their trench, and snipped off samples to present to their superiors:

'That went on every night and the old man never knew we had a coil of Jerry wire on our side'

A British sergeant

'Live and Let Live' contradicts the usual view of trench warfare as an unceasing torment of mud and bullets. Soldiers occasionally worked across the lines to thwart their officers' intentions and minimise the dangers they faced. If it wasn't the international brotherhood that socialists had hoped for in 1914, it certainly demonstrated that the enlisted men were more than simple automata who blindly followed their superiors' orders. In 1917, this desire for freedom of action would find expression in two revolutions in Russia, in French army mutinies, and in the desertions and mass surrenders of Italian troops. It was the ordinary soldier's way of turning his back on the war.

Game Theory on TV

This is a great clip from the ITV Game Show Goldenballs hosted by Jasper Carrot. It is about 10 minutes long and the last three minutes are the most relevant. The first seven simply set up the game and lead to the climax.The game is a variation of the Prisoner's Dilemma, though there are major differences.

The similarities are: 1. It is a game of cooperation (share) or defection (steal). 2. Decisions are made simultaneously.

The major differences are: 1. This is a zero-sum game. 2. The players can communicate.

 

Here is some analysis of the decisions involved. Assuming a jackpot of £100k the following outcomes are possible:

 

		PLAYER TWO
		Split	Steal
PLAYER ONE	Split	50k, 50k	0, 100k
	Steal	100k, 0	0, 0

The worst outcome in this game is for the players to both choose ‘steal’ as that would mean no one wins the jackpot. All other scenarios mean the full jackpot is given to at least one of the players. At initial inspection it may appear that the jackpot will be given out ¾ times and no jackpot a ¼ of the time. But the interesting thing with this game is that assuming all players behave rationally the outcome will actually always be that no one wins the jackpot (i.e. two steals).

If you put yourself in the position as a player, you can see how this works. There are two possible options that your opponent can choose (‘steal’ or ‘split’).

Take scenario 1 where your opponent chooses ‘split’. Here if you choose ‘split’ you will get half the jackpot, if you choose ‘steal’ you will get the entire jackpot. So obviously any rational person will choose ‘steal’ as this will maximise your winnings.

Take scenario 2 where your opponent chooses ‘steal’, in this scenario it is irrelevant whether you choose ‘steal’ or ‘split’ because either way you will get nothing. So given the scenario 2 decision is irrelevant (as ‘steal’ and ‘split’ both result in 0) your decision should be based purely on scenario 1 where it has already been illustrated that any rational person will choose ‘steal’.

So the optimum strategy for any player is ‘steal’! Of course the problem with this is that your opponent has the same options as you and therefore will pick ‘steal’ which means the game ends in two ‘steals’. So going back to the game show assuming that all participants are rational human beings the first 55 minutes of the show are irrelevant because whatever the jackpot ends up being the result of the game will always end up with no one wining anything (if the players act rationally).

Play the Prisoner’s Dilemma

This is an excellent application of the Prisoner's Dilemma.

You get to play against five different "personalities". Can you figure out your opponent's strategy? Do you cheat? How do you ensure cooperation? These are all problems of the Prisoner's Dilemma. Run through this a few times and you will have a better grasp of the elements involved.

Click here to play.

Game Theory in Films

There are loads of clips depicting game theory from popular films. Here are just three.

First up is the fictional clip from from A Beautiful Mind in which John Nash uses the dating (or should that be mating?) game to suggest that Adam Smith is in the need of a slight revision.

 

Here is the Game of Chicken from James Dean's Rebel Without A Cause.

 

Here is a clip from Stanley Kubrick's brilliant film Dr. Strangelove. This classic clip explains the concept of a credible commitment, highlighting the importance of clarity, irreversibility, and public knowledge.

Rock, Paper, Scissors

The simple game of Rock Paper Scissors can be used to analyse many of the properties of two-person zero-sum games. The following image gives the outcomes of the game.

Here is a payoff matrix for the game. The first number in each cell is the payoff to the row player. The second number in each cell is the payoff the the column player.

The payoffs are zero if the game is tied, +1 to the winner and -1 to the loser.

	Rock	Paper	Scissors
Rock	0, 0	-1, +1	+1, -1
Paper	+1, -1	0, 0	-1, +1
Scissors	-1, +1	+1, -1	0, 0

Here is a winning strategy for the game

Game Theory in the print media

Examples of Game Theory in the media are almost endless. This is because individual decision making is hugely interdependent. Have a browse though some of these newspaper articles that illustrate game theory at work. It might be best to print them out and write notes on the game theory aspects that arise in each.

Here is a Financial Times piece by John Kay on the Battle of the Sexes and this from the same author on the Game of Chicken.

Andrea Farina is the 2007 World Rock Paper Scissors Champion. I kid you not! ESPN have announced that they are going to televise the RPS Championships! And the 2008 World Champion is Irish.

This is what can happen if firms get caught colluding. But of course countries are able to collude and get away with it. Although slightly dated this piece gives a good idea of what OPEC is all about. The BBC report here shows how a coffee equivalent to OPEC was less successful.

It may seem I have a strange fixation with NASCAR but this article from Slate manages to link car racing and Game Theory. It is actually quite credible as racing is by its nature strategic - watch the end of Days of Thunder for proof. Oh go on, you know you want to. Here it is courtesy of YouTube and remember "Cole always goes high!"

Poker has seen a huge increase in its popularity recently. This piece gives an easy insight into the Game Theory fundamentals of games such as poker and tries to convince that a computer can make the best player. Those who want to add a little Game Theory to their poker game should read this. A nice piece on poker by Tim Harford can be found here and finishes with the suggestion that online poker may be threatened if a winning computer poker player can be created.

See why drug taking is a Prisoner's Dilemma in sports and find out here the strategy involved in Penalty Shootouts.

This piece from The Business Journal uses Game Theory and The Matching Pennies game to exlain why you can't beat the stock market over the long run.In this piece stock's markets are compared to newspaper beauty contests.

There are thousands of more examples but the above selection should give you a taste of what's out there.