Archive for April, 2012

Goldenballs, the prisoner’s dilemma and how Ibrahim could have won it all

This clip of an extraordinary game of Goldenballs has been doing the rounds recently, and as I’ve been brushing up on my micro, I thought I’d do a little guide to how it worked.

The idea of the game Goldenballs is based on the Prisoner’s Dilemma in game theory. In this dilemma, two prisoners are arrested and questioned by police. They have two options, Silence or Betrayal. If they both choose Silence, they both are let free. If one chooses Silence and the other chooses Betrayal, then the Betrayer gets a new life in Monte Carlo, while the Silent one is locked up for ten years. If they both attempt to grass up the other, then they both get 5 years in jail.

Let’s put some numbers on to this. If we have person x and person y, then the payoffs are

<Silence, Silence> <5, 5>

<Silence, Betrayal> <-10, 10>

<Betrayal, Silence> <10, -10>

<Betrayal, Betrayal> <-5, -5>

The idea of the game is that there is an equilibrium at <Betrayal, Betrayal>, even though both players would be better of at <Silence, Silence>. This is because, if you think the other person will remain silent, your payoff is maximised by betrayal (5 < 10) and if you think the other person will betray you, your payoff is maximised by betrayal too (-10 < -5). Therefore betrayal is a dominant strategy for both parties (This is the most basic problem in game theory, so although I haven’t used any grids etc a quick google can put you straight if you’re still confused).

The problem is you have no way of co-ordinating your decision in this one-shot game. Goldenballs introduces a co-ordinative aspect, by giving the participants a chance to discuss their decision. And normally it takes the form “We should co-operate”. “Yeah we should.” “Cool let’s co-operate then” then a question of how honest the people are.

But, as Mr Right (the player’s in this game I’m going to call Mr Right and Mr Left, I’ve decided) has worked out, such an attitude to negotiation doesn’t solve the game. The dominant strategy to betray remains, and the Nash Equilibrium of <betrayal, betrayal> does too; regardless of the good vibes you’ve been getting from your partner through out the game. The incentive is still there to steal.

BUT… this is not the same game as outlined above. The payoffs are:

<Split, Split> <6,800, 6,800>

<Split, Steal> <0, 13,800>

<Steal, Split> <13,800, 0>

<Steal, Steal> <0, 0>

If you think the other person is going to Split, there is a clear incentive to Steal. But if you think they are going to Steal, then you are faced with the payoffs of 0 or 0. They are equivalent. Thus, Steal is only a weakly dominant strategy.

Rather than engage in the fantasy that co-operation was possible if Mr L thought R was going to Split (faced with such a proposition, L would always steal), Mr R sets his stall out: I’m going to steal. This infuriates L – he can’t do anything with that. Whatever he does, he’ll get nothing.

But Mr R offers him a chance of the winnings. Although this isn’t taken very seriously by Mr L, it is (quite literally) better than nothing. His payoff from Splitting if Mr Right steals is now 6,800p, where p is the probability that R keeps his promise. p could be infinitesimally small, but as long as it isn’t zero, it’s better than the alternative.

This is presumably the realisation that L has when he sighs “okay, I’m going to go with you.” He splits, so does Mr R, and co-operation in a one shot game has been achieved.

Is this the only solution to the game? Quite simply, no. Mr R constructed a payoff matrix whereby L had nothing to lose by splitting, but the uncertainty in whether or not Mr R will keep his promise is only uncertain to Mr L. Mr R knows exactly what he’ll do. Let’s call “altruistic” Mr R “Nick”, and evil Mr R “Mick”. If Mr R is Nick, then he may as well play Split too, as p = 1, so his payoff from Stealing is 13,600-6,800 = 6,800, so Split and Steal are equivalent. We could even model a negligible benefit ε of being an internet hit and people knowing how nice you are, so his payoff from splitting is slightly higher. But Mick would do no such thing, and would steal the money and then not share. Then he has to play steal, and once he had, even though on the show we wouldn’t know if he would keep his word, we can assume he won’t, as if he was going to cough up he may as well as split. So for what happened to be a proper solution to the game, we have to make assumptions about the nature of Mr R, and his utility gain from (essentially) being nice (perhaps the size of ε).

But Mr L didn’t play in a totally rational manner either. Because rationality means that one can, essentially, work out everything that I’ve just written above before the game is played. And even though L didn’t know who he was playing, evil Mick or nice Nick, he would have been rational to steal in either case. Mr R’s promise is not credible, not just because once he’s one the jackpot no-one can make him share it (a classic intertemporal problem, which I won’t go into here…) but because, as outlined above, an altruistic Mr R (Nick) would just play Split. At which point… Mr L has an incentive to Steal the whole jackpot! So in fact, even though Nick created a payoff matrix for Ibrahim (aka Mr L) where he only had something to gain by Splitting, had Ibrahim thought through the motivations of what Nick was saying, he would have found it rational to cheat. Perhaps Ibrahim didn’t have enough time to think it through, and Goldenballs’ time limit saved Nick and his altruism.

But perhaps Ibrahim is just as irrational as Nick. As they both had a chance to win it all, and neither took it. In a one-shot game, there can be no future punishment, no way of enforcing agreement. So ultimately, although Nick’s strategy seemed to create new payoffs for Ibrahim, its success rested on trust and a belief in non-rational altruism all the same.


Institutions, experiments and the resource curse

Previously I mused about whether or not the East African countries who have recently discovered natural resources would be able to make the most them, to benefit their country in terms of GDP and also on a broader scale.

Now a bit more on how that resource curse supposedly works. Robinson, Torvik and Verdier (2006) have argued that the political incentives that are generated by natural resources (as opposed to purely economic ones) are key to  understanding why certain countries have resource curses and why others don’t. Rather than a static explanation unable to explain variation in outcomes across countries, such as Dutch Disease or even rent-seeking models (where pressure groups force their government’s hand in granting them concessions), Robinson et al argue that variation in institutional quality can help explain the presence or lack thereof of a resource curse. Moreover, Mehlum et al. (2006) have shown empirically that once you’ve controlled for the interaction between institutions and resources, it turns out that resources positively affect growth with good institutions, yet the “curse” sets in when institutions are bad.

So it’s worth measuring the institutions of Uganda, Kenya, Tanzania and Mozambique, to try and ascertain who might make the best use of their resources. Looking to precedence, Abidin (2001) claims that Botswana, Chile, Malaysia, Oman and Thailand have successfully escaped the resource curse, while Algeria, Ecuador, Mexico, Nigeria, Saudi Arabia, Trinidad and Tobago, Venezuela and Zambia at that time were still unable to do so. Using Sachs and Warner’s index of institutional quality, Robinson et al verify that those who have escaped the resource trap according to Abidin have good institutions according to Sachs and Warner.

The Sachs and Warner dataset is quite old nowadays, so I’m going to use the Corruption Perceptions Index for 2011 as a proxy for institutional quality. Imperfect as this is, it verifies that the countries that have escaped the resource curse, according to Abidin, are less corrupt. The exception to this is that Saudi Arabia; according to the score, it is better for transparency than both Malaysia and Thailand (I’ll return to concerns about the score at the end).

Right, so with all this in mind, how might our East African countries, newly endowed with natural resources, perform, if institutions, represented by CPI score, are predictive or determinative of resource management?

It’s marginal, but there are differences across the countries. With a rating of 3.0, Tanzania performs the best on the CPI, followed by Mozambique on 2.7, Uganda on 2.4 and Kenya on 2.2. Historical context helps to explain this: Julius Nyerere keenly strove to reduce ethnic tensions in the name of national unity, whereas leaders such as Daniel arap Moi exploited divisions. While Kenya outperformed Tanzania in economic terms for much of the post-independence period, it appears poorly positioned compared to Tanzania to manage its resource wealth effectively, as this history of maintaining power through blatantly neopatrimonial networks is exactly the mechanism that Robinson et al argue translates poor institutions into a resource curse.

So tentatively, we might think that Tanzania is the least likely to be cursed by their resources, whereas Kenya could face serious problems in resource management. But… it might not be all as simple as that. Take Angola Angola scores an incredibly low 2.0 on this corruption perception scale. However, according the Economist, Angola grew at an average rate of 11.1% last decade. The resource curse is usually couched in terms of growth (see eg, Collier, 2008). Even Abidin calls it a “low growth staple trap”. But few people would say that, given its growth, Angola has no issues in relation to its oil management; it’s not Norway. In a previous post, I said that reduction of poverty or inequality should be taken to account in assessing how well a country manages its resources, and Angola certainly fails on that count.

It’s also a puzzler for Robinson’s theory, as even if we reckon GDP isn’t the be all and end all, his theory suggests that growth shouldn’t even be sustainable with poor institutions. Perhaps the intertemporal bias cited by him towards consumption and spending today means that GDP figures are being inflated for the moment, only to see a crash later. As such, Angola hasn’t really escaped the resource trap, and might be approaching a crash when the oil dries up/if oil prices fall. But a decade is quite a long time for growth to be sustained if bad institutions are meant to be prohibitive to growth.

This is one of the reasons why the experience of the East African countries should be so illuminating. Angola had one thing which no other country had when they discovered resources – a civil war. Hence in the decade since the civil war ended, it might not be surprising that the economy grew rapidly; it escaped the conflict trap, regardless of whether or not there’s a resource trap. Moreover, previous studies that thought Angola’s institutions were harmful to their resource management might have been picking up the effects of conflict.

With four similar countries all discovering resources at a similar time, hopefully we’ll be able to have a more “scientific” take on the effect of natural resources, rather than drawing too many conclusions on the basis of a unique case in Angola, which has a lot of other things going on which may be helping or hindering growth.

Either way, the Angolan case shows that while poor institutions may be conducive to a resource trap, they are not sufficient for one, at least to the extent to which the “trap” is defined in terms of GDP. Which must be encouraging to the leaders of Kenya, Mozambique, Tanzania and Uganda, as none of the countries score especially well on the CPI. However, if it means these countries can insulate themselves from domestic discontent and fuel GDP growth while ignoring much of the population, it may be less encouraging to their people.

Who said what? Round One: Sir Alex Ferguson vs Comrade Nikita Khrushchev

“Dissent is for losers”, apparently: an outlook that Sir Alex Ferguson happens to share with Nikita Khrushchev, former First Secretary of the Soviet Communist Party.  And it’s not the only one. Couple that with their beautiful mugs, and it can be hard to tell them apart. So, who said it, Fergie or Nikita?

1) “We have to swallow this bitter pill… The weak complain against the strong; the strong pay no attention and continue their insolent action” – Fergie, upset at Thierry Henry’s 90th minute winner in a 2007 league game OR Nikita, after the Soviets failed to shoot down a US spy plane?

2) “He could start a row in an empty house.” – Nikita on Lyndon Johnson, OR Fergie, on Dennis Wise?

3) “He was certainly full of it, calling me “Boss” and “Big Man” when we had [a] drink… But it would help if his greetings were accompanied by a decent glass of wine. What he gave me was paint-stripper.” – Fergie on José Mourinho after a Champions League game, OR Nikita, after a landmark meeting with Dwight Eisenhower at Camp David?

4) “We will bury you” – Nikita, referring to agents of international imperialism, OR Fergie, referring to Roberto Mancini’s Man City?

5) “If you start throwing hedgehogs under me, I shall throw a couple of porcupines under you” – Fergie, speaking to the media, OR Nikita, speaking to the media?

6) “Sometimes you look in a field and you see a cow and you think it’s a better cow than the one you’ve got in your own field. It’s a fact. Right? And it never really works out that way.” – Nikita, in reference to why East Germany would regret reunification with its seemingly more prosperous neighbours, OR Fergie, in reference to Wayne Rooney?

7) “[This] question has stuck like a dead rat in the throat of some people – they are disgusted with it and yet they can’t spit it out” – Fergie, when asked about the BBC’s allegations about his son Jason, OR Nikita, when asked about Soviet intervention in Hungary?

8) “Though you are a fiery young man and I am no longer young, I can still compete with you” – Nikita to an American talk show host OR Fergie in a touch-line encounter with Andre Villas-Boas?

9) “[so] I decided to add a little more heat. I took off my shoe and pounded it…” – Fergie, in reference to David Beckham’s forehead, or Nikita, as he made a point about General Franco?

10) “They are the inventors of the smokescreen.” – Nikita, in reference to Americans, OR Fergie, in reference to Italians?

11) “He’s not [x], he’s a piece of shit” – Fergie, (missing words “the Great One,”) in reference to Jose Mourinho, OR Nikita (missing words “the foreign minister”) referring to the Soviet foreign minister?

12) “He’s a bully, a fucking big-time Charlie”. Nikita, referring to John Foster Dulles, Eisenhower’s Secretary of State, or Fergie, referring to Paul Ince?

13) “Could that come under the description ‘desperation?’ I’ve got plenty of ammunition, don’t worry. They can try.” Fergie, speaking figuratively in reference to Carlos Tevez playing again for Man City, or Nikita, speaking literally about a possible NATO-led military solution to the Berlin question?

14) “What am I going to do without work? How am I going to live?” Nikita after his very real, enforced retirement OR Fergie musing on his potential, always-imminent but never arriving theoretical retirement?

15) ‘It’s getting tickly now – squeaky-bum time, I call it.’ Fergie, in reference to the tension of the end of the season, or Nikita, in reference to the tension of the potentially world-ending Cuban Missile Crisis?

Answers in the comment below…

An inglorious triumvirate

I’ve had some interesting feedback to my last blog post, some of which took it more seriously than intended but all of which is well taken (not least as I’d be hypocritical to defend lazy blogging with appeal to humour given my unforgiving post of the same day). The central point of the post is the use of discourse: when the economy is recovering, it is due to the government’s genius, when it is tanking, it is due to all manner of implausible, irrelevant  and highfalutin excuses. And that point still stands.

The claim that the panic was purposively induced was meant more ironically, which is just as well because, as has been pointed out to me, the figures don’t add up. ONS statistics of Q4 GDP at market prices have £380,517,000 = 0.1% of quarterly GDP, meaning that to add +0.3% (assuming 0% growth without the fuel crisis) would require >£1.1bn extra spending. If we assume 30 million cars on the roads, they’d all have needed fill up at the government recommended amount of half a tank (30 litres) at 140p per litre, and it not had had a negative impact on other consumption. In one sense this is possible, as the nature of panic buying isn’t that everyone followed the government’s “reasonable” advice, but that those who did top up bought much more than half a tank, even if it wasn’t all the 30 million. But then wrangling like this is tenuous, as how many would had to have bought petrol anyway, how many people at petrol stations across the country who were interviewed by the BBC exclaimed their frustration at the panic buying while claiming (very plausibly) that they needed it? Analogously you can argue that the supposed growth of last quarter was illusory because the the proportion of money that is spent on food… clearly that is absurd. My point was that the government’s reasoning is likewise tenuous, and had growth been below par they probably would have cited Lent and a drop in demand for sugar as the reason, even though it’s never been relevant any other year, and people buy Easter eggs preemptively…

Whatever, you get the picture. Given the difficulty of working out the effect of the petrol crisis on growth, the idea that it was pre-planned conspiracy is far-fetched to say the least. Irony is hard to convey on a blog, and while I don’t apologise for that, I did want the figures and will happily admit that they don’t back up the hypothesis of coalition led conspiracy. But part of me thinks: if only they did! Because as explanations of accounting for the government’s motivation during the the petrol crisis, we have that it was:

a) a conspiratorial account for inflating growth figures,

b) a possible “Thatcher moment”, spoiling for a fight with trade unions

c) due to massive amounts of governmental incompetence.

The friend who alerted me to the figures cited b), I’d just as happily believe c). Inflating growth figures, while underhand, could instrumentally benefit the country, restoring market confidence and perhaps creating a positive cycle of growth. While we have a classic case of credit-taking by the political class, good things could come of it, and frankly, it seems the lesser of three evils when explaining the government’s action. Which might be, in term, why on examination it’s the least plausible. After all, of all the feedback I had from the blog, no-one said that I was being unfair on the government per se; merely that I had misidentified their motivations, and the exact nature of their dastardliness/incompetence. Which doesn’t exactly cover them in glory.

Tanker Politics and Technical Recessions

As is repeated to the point of banality, a week is a long time in politics. Last week, the OECD said that Britain would fall back into a technical recession. This week, the BCC said it will avoid one. What’s changed in the interim? Well, the exogenous consumption shock of a manufactured crisis that hugely increased demand for an expensive product during the last few days of Q1, that’s what.

Whenever the performance of the economy has been below par, there’s always been an excuse. The royal wedding.  Cold weather. Warm weather. But now we have a mightily impressive growth rate of 0.3%, it’s not the result of chaos and panic induced by the government, but rather is “encouraging”, and proof of business “confidence”. Much like the reaction to the budget was meant to be. How dim do they think we are? “Oh, GlaxoSmithKline read the budget and overnight decided to create a thousand jobs! What a good budget that must be. And when George Osborne gets asked questions about things like the 50% tax rate, he can legitimately cite GSK (despite its lack of relevance) and I will be satisfied.” (See 1.20-2.10ish).

You have to hand it to the government, it’s all fairly ingenious. Want a good way to boost consumption without giving anyone a job or more income to fund it? We’ve just been shown a masterclass. And it’s not even as if  all the petrol will go to waste! We just all bought it a few days early, and can keep it in those trusty jerrycans in the interim.

Schrödinger’s Romney

David Javerbaum has quite a fun piece in the NYT about a “Quantum Theory of Mitt Romney”. And when I say “quite fun”, I mean “wrong about most things”. He gamely tries to apply principles to quantum physics to Mitt Romney’s campaign, but, while entertaining, he makes some claims which even tongue-in-cheekness can’t excuse.

Firstly, Newt Gingrich as a “traditional campaigner”? I understand that the “Newtonian” pun was too good a chance to miss, but the idea that Gingrich is the prototypical candidate, whose “position on an issue tends to stay at rest until an outside force — the Tea Party, say, or a six-figure credit line at Tiffany — compels him to alter his stance…” is absurd. A colony on the moon: what the Tea Party have always wanted! Regardless of whether he was pandering to the Florida electorate in that instance, the extent in which he flip-flops for more “rational” or less “random” reasons than Romney is highly dubious.

More egregiously, there’s then this non sequitur on the issue of non-causality

For example, ordinarily the cause of getting the most votes leads to the effect of being considered the most electable candidate. But in the case of Mitt Romney, the cause of being considered the most electable candidate actually produces the effect of getting the most votes.

Pretty much every election I can think of has causality running from being considered the most electable to then getting the most votes. Ordinarily, the cause of getting the most votes has the effect of being, urm, the elected candidate, not the most electable one. I understand that the repeated game scenario of a primary season complicates this, but come on, it’s simple Downesian stuff, and the idea that being considered electable leads to your election doesn’t need an appeal to sub-atomic chaos to explain.

There’s a whole other point about the sentience of subatomic particles, and how they couldn’t settle on a state that is “likely to please the asker” in the way that Romney does, as that wouldn’t be random… Anyway, I won’t do any more on this; I get it’s a joke, and my soul aim in life isn’t actually to destroy all that is light-hearted and carefree with overblown pedantry. But there is a more serious point here. Why is Romney considered a uniquely unknown politician? Why so much speculation over who is “the real Mitt Romney?” He seems to me to be going through the same juggling act that most candidates go through; of appealing to a primary base that is more extreme than his (presumed) electorate for November, and he tries to say things to please a broad range of diverse people. And you can’t always take what he says at face value? Shucks, he’s only a politician after all.

Although I guess, to be fair on Javerbaum, appealing to a broad range of people would certainly set him apart from Newt.