Why dictators should study Game Theory!

One of the (over)hyped features of the revolutions in the Arab world has been the role played by social media. Several articles have outlined how social media have made spreading information much faster, which has helped mobilize people to protest against the regimes. This is particularly important since these countries do not have an independent "regular" media.

However, overcoming the "coordination" problem is just one of the 2 problems that an individual faces in deciding to protest against the regime. For an individual to decide rationally that he can protest he needs to overcome 2 problems of information asymmetry

1. The "coordination" problem: Where and when the protests will be held
2. The "common knowledge for confidence" problem: For me, as a rational individual, to decide to protest, I need to know there are several other protesters. The reasoning is simple, if I am going to be one among only a handful of protesters then the dictatorship would crush the protest ruthlessly. If on the other hand I am among half a million protesters the dictatorship would be unable to do so.

Note that every individual faces the same issue. Hence what is required for a successful protest is that I know there are other protesters, and that they know the same. They should know, that I know, that they also want to protest and I should know that they know the same. Hence there should a "common knowledge" about the desire to protest for me to be able to have the confidence to protests myself. 


The role of social media is actually as important in overcoming the latter, as the former problem. When I post about the protest on Twitter or Facebook, and someone "Likes" or Retweets my message, we automatically have common knowledge.

The answer, if you are Mubarak, seems intuitive, shut down social media! However, with a little game theory you can show that this would actually be counterproductive! (the Game Theory blog "Cheap Talk" showed this well in their post http://cheeptalk.wordpress.com/2011/01/28/cutting-off-communications-in-egypt/. However they have not talked about the former problem, and how shutting down social media would affect that )

The reasoning is as follows. The regime would not shut down social media unless their assessment was that the protests could be large-scale. But this is precisely the information that i as an individual protester seek!- whether the protests are going to be large-scale or not (and that everybody else is aware of the same!), because that is when it is rational for me to protest too! In other words, the regime has successfully consolidated all the private signals of protest, into one big public signal. Hence, paradoxically, the act of shutting down social media makes its role even more efficient in terms of overcoming the "common knowledge for confidence" problem- everyone instantly knows that everyone else is keen to protest and that they all know the same!

But, hang on, would it still not achieve the purpose of preventing the protesters from overcoming the coordination problem (the first problem outlined above)? Granted, they all now have the confidence to protest, but in the absence of social media, how would they know when and where to go? In which case, isn't shutting down social media still effective?

The answer is No, and it is due to a concept called "focal points" (which was first popularized by Malcolm Gladwell).

Consider this thought experiment: If I told you that you were supposed to meet someone in Paris the next day. I do not tell you the time or the place. The only thing that you know is that the other person has the same information. What would you do? Most people would decide to go to the Eiffel Tower at 12 noon. This is because when we have to solve coordination problems in the absence of information there are some "default" solutions that we inexorably converge towards, as we expect others to arrive at the same default solution.

Hence, when social media is shutdown, and I know there is no way to communicate with my legion of fellow protesters (I know it is a legion now by the regime's act of shutting down social media), I will protest in the famous focal point-  namely, Tahrir Square at 12 PM!

Note, that again the act of the dictatorship has been counterproductive- it ensures that every single protester converges upon the focal point, where it might have been that they would have been more dispersed otherwise!

S the act of shutting down social media helps the protesters solve both the coordination problem and the common knowledge for confidence problem, more efficiently, and optimally, than they otherwise would have!

But what should the government have done? Not doing anything would have still led the protesters to solve the problem using social media.

There were 2 options to consider. One is that given that the protesters would necessarily converge upon the focal point, to focus only on preventing people from getting there e.g., in blocking key arterial roads to Tahrir Square.

The other option is to use misinformation. Just as bad money drives good money out of circulation ( Gresham's law), bad information would drive good information out of circulation, if the Government had used social media to spread rumors about the size and nature of protests, and confused people with multiple and contradictory views of where protests would occur, that might have helped. this is however difficult to pull off since people typically automatically have a quality filter in social media networks (since you decide whom to follow or friend).

The collapse of these repressive regimes was inevitable, but by their ham handed actions driven by lack of knowledge of Game Theory, they hastened their own demise. Cheers to that!

Orders of rationality?

One of the fascinating problems of Game Theory is the Traveler’s Dilemma, a variant of the classical Prisoner’s Dilemma situation -where rational actions by individuals to maximize individual welfare leads to sub-optimal outcomes for each of them.

The game design is as follows: (Reference: Traveler’s Dilemma by Kaushik Basu, Scientific American:
link: http://www.sciam.com/print_version.cfm?articleID=7750A576-E7F2-99DF-3824E0B1C2540D47)

Lucy and Pete, returning from a remote Pacific island, find that the airline has damaged the identical antiques that each had purchased. An airline manager says that he is happy to compensate them but is handicapped by being clueless about the value of these strange objects. Simply asking the travelers for the price is hopeless, he figures, for they will inflate it.
Instead he devises a more complicated scheme. He asks each of them to write down the price of the antique as any dollar integer between 2 and 100 without conferring together. If both write the same number, he will take that to be the true price, and he will pay each of them that amount. But if they write different numbers, he will assume that the lower one is the actual price and that the person writing the higher number is cheating. In that case, he will pay both of them the lower number along with a bonus and a penalty--the person who wrote the lower number will get $2 more as a reward for honesty and the one who wrote the higher number will get $2 less as a punishment. For instance, if Lucy writes 46 and Pete writes 100, Lucy will get $48 and Pete will get $44.
What numbers will Lucy and Pete write? What number would you write?

The solution to the problem is that each would choose $2 as the value of the antique-hence getting only $2 each! Also, this is a dominant solution (i.e. it is the strategy to be adopted, not just one of the strategies)

Note: For the detailed proof visit the link given above

Now if $2 sounds ludicrously low….you’re right! When the Traveler’s Dilemma game was administered on actual players most players chose $100 or a number close to that rather than $2 though, by the tenets of Game Theory they ought to have chosen to play $2. And by deviating from the rational choice, they were better off!

Other fascinating aspects include how strategies changed with the change in reward/penalty, and on repeated play.

Why would people deviate from expected rational behaviour. Three possible explanations have been offered: irrationality, rational altruism and meta-rationality (Usage:mine).

The first explanation, that players were simply ignorant or unable to deduce the ‘correct’ strategy might be true in some cases but was dismissed as a general explanation since even Game theorists who arrived at the dominant (2,2) solution, chose to play a number close to 100.

The second explanation is based on the premise that in the real world people do not want to ‘cheat’ their partners to make an extra buck-, that some degree of “altruism” and a sense of “fairness” is hardwired in all of us.
As an insight, it is extremely useful, but the implications are simple to factor in, it wil involve just tinkering with the utility function ( a function that maps actual winnings to the ‘utility’ that players assign to them). Right now, the utility function is a simplistic f(x)=x, i.e. if I earn $50 it is ‘worth’ $50 to me, now we will have to design utlity functions which are a function of not just our earnings but possibly that of the other’s earnings ( “altruism”) and/or of the difference between earnings ( “fairness”). Constructing such utility functions by analyzing actual moves by players could be a very interesting empirical research study. However, is this explanation correct? Even if we control for this effect, is it possible that players will still opt to play an ‘unexpected’ strategy.

Which brings me to my favourite explanation- the second one, wherein lies the most fascinating insight (its fascinating for me- I came up with it! ),that of ‘orders of rationality’

‘Orders of’ something, is the level at which it loops back at itself. If that seems complex, think of the Friends episode where Rachel and Phoebe discover that Monica and Chandler are involved, and want to ‘play’ a prank on them. Set 1( Monica and Chandler) have first order knowledge- they know they are involved and have no idea what Phoebe and Rachel ( Set 2) know, whereas Set 2 has second-order knowledge since they know, AND they know that Set 1 doesn’t know that they know. ( Note: This brings out the distinction between not knowing that the other set knows and knowing that the other set definitely doesn’t know; absence of evidence is not evidence of absence).
As the episode goes along, successively the orders of knowledge possessed by each Set increases ( Chandler and Monica find out that Phoebe and Rachel know( which Phoebe and Rachel don’t know!) and decide to play a prank themselves ( in the words of Chandler : “The messers become the messees!!”) and this continues).

In a Game Theory situation, knowing the rules of the game would be first order knowledge, knowing that the other player knows the rules of the game is second order knowledge, knowing that the other person has second order knowledge is third order knowledge ( or more generally- knowing that the other person has nth order knowledge is (n+1)th order knowledge). If this process continues ad infinitum(if you are not Joey, you can conceive of this!), the players are said to have “common knowledge”. Most games ( even the simple ones like the Prisoner’s Dilemma) have a premise of common knowledge. Common knowledge, is hence, an infinite stack of the orders of knowledge.

Can we then conceive even of rational behavior- a basic premise of game theory, and indeed of economics in general, as a stack of decisions rather than as a one-shot one.

To make it more clear, consider this: we human beings have the ability to think about our thinking ( We do it all the time “ I was not thinking straight when I said that”; “ When I think about incidents, I find I index them by date”; “ I think about sequences more easily than I do of individual entities” etc). This thinking about thinking (or meta-thinking to put it more elegantly) is very interesting- we can ‘step-out’ of a mode to look at our own thought processes at a higher level of abstraction. This leads us to the next insight, that, similarly, we could also be deciding sequentially. (I can meta-think to about 4 levels, after that my head starts to hurt!).

So does the solution to the Traveler’s Dilemma puzzle lie in the insight that we can rationally decide to act rationally/irrationally! (To put it more vividly, to accurately reflect the sequential process- can we META-rationally decide to act rationally/irrationally). This is consistent with what players said that they knew that rationally they ought to have played 2 but they chose to ignore rationality in making the choice ( citation: Kaushik Basu).

This has far more profound implications for the way we study Game Theory. Unlike the previous explanation, which also challenges a basic premise of Game Theory ( i.e. of selfish rationality) but can easily be made endogenous to current literature merely by changing the functional specification of utility, this would radically alter the way we approach the problem solving in the abstract, and would require an entire supporting theory ( as opposed to mere empirical work) which discusses the orders of rationality and how at meta-rational levels, choices of rationality and irrationality are made.