The Moorish Wanderer

Game Theory & Revolutions

Posted in Flash News, The Wanderer, Tiny bit of Politics by Zouhair ABH on February 5, 2011

True to my word to Afrinomad, I’ll try and  delineate the game theory applications on revolutions. I’ll go slower, not the least because it’s uncharted territory there to me. I mean, the best I’d ever do with game theory is with economics application -just like the mess I am supposed to sort out by this spring-. This does not mean I don’t understand what I should be posting about. Let’s just say that there are some areas in political sciences I would do well to read about on my spare time (oh? Do I still have one of these?)

Looking back at the undergraduate days, I read an interesting book, which turned out to be a big helper in understanding political sociology: ‘Théorie du Choix Révolutionnaire‘ (T.Tazdaït, R.Nessah La Découverte, 2008). It is handy, in the sense that both authors are at ease with game theory concepts. And one of the many things I noticed -and recorded- was the constant reminder that revolutions, in essence are not really a rational behaviour. Why should it be? The whole idea of mixing revolution theory and rationalism seems ludicrous: not that both concepts are irreconcilable, but because that a pure rationale, from an individual point of view, collective action is deemed to failure. Shaw proposed the following the illustrate the paradox: let the following linear equation be an agent’s utility function R = p.B – C + D

It's already there, mate.

where R is the utility pay-off, p is the probability assigned to the effect the individual can have on a successful outcome for the revolution, C the cost of participation and D the expected pay-off. Before I go any further, this is not a normative model, in the sense that it should not elicit conclusions about what’s a good or a bad revolution. At best, it’s an abstract speculation on rationale behind individual and collective behaviour. Now, if there are masses of people supporting the revolution, an individual contribution to success is next to nothing. Plus if the individual does not participate, they incur no cost and benefit nonetheless from the revolutionary outcome. But if the same result was to be applied to every single member of the community, the revolution is doomed before it even begins. So there is the nodal problem: Revolutions are the deed of the multitude. And yet, when individuals weight in the costs and benefits, they have every incentive to adopt a free-rider behaviour: wait by and look on as he events undo the incumbent regime, then reap the benefits when it succeeds. If not, being obedient brings benefits too.

This ultra-rational behaviour does not explain why revolutions occur. In fact, it just makes people think that revolutions are inherently irrational. But are they? Perhaps this individual methodology is no good to understand collective action: it is logical to assume that the collective effort is not a mere aggregation of individual wills, that, past a certain critical mass effect, it subsumes it and exceeds to a greater strength.

Let’s find us some practical game theory application on Egypt and Tunisia: assume the revolution is a public good – there’s an interesting configuration by Vickery-Clarke-Groves which seems to me suitable for collective actions. In a game theory setting, for a revolution to succeed, it needs to devise some modus operandi following which the result would be strategy-proof, i.e. at some stage, all individuals would contribute to the outcome according to their true needs, and as such their benefits would be larger in contributing to the revolution than just standing out of it, when they would indeed benefit from a change of regime. Let me re-formulate it: there’s a need for a modus operandi such that those really in need for a revolution would in fact contribute rather than just stand by. These very individuals, the least endowed in a given society that is, have every incentive to revolt because the expected loss is considered to be lower than the benefits.

So, a public good, or a revolution, seeks the modified optimization program:

it’s easier to understand than it looks actually – the revolution seeks increasing the well-being of the majority -thus the mode- (first line) but takes ‘taxes’ out of different individuals (second line), and these taxes can be perfectly random, like death, or an injury or just a burned car. k is the last outcome: success (1) or failure (0). Then, at individual level (third line), they have types that are more or less attached to a change in the political regime or indeed achieving any desired outcome the incumbent government does not provide. Insofar the poorest elements have the lowest tolerance for a certain array of imbalanced distribution of wealth, income, power and other social symbolism outlets, they can be expected to react and contribute -issues of coordination are not discussed here- because in Egypt or Tunisia their numbers were important, the contribution of middle classes was perhaps marginal at the second level, but it nonetheless gave a larger boost to the public good. The game has a social choice function f(.) fully strategy-proof as long as it meets the following requirements:

basically, a function that yields a utility such that it is better for an individual to act following their type rather than portray another one (called the incentive compatibility).

When the coordination issue is not discussed, the key for revolutions, from a game theory perspective, is to ask first off, how wide is the gap between expected gains the rioter, soon-to-be revolutionary, is betting on, and their present wealth, and second, how many of them are ready to join in, i.e. how many are in the same position.

When coordination does arise, it can either be the fact of institutional nature -which game theory has little to do with- like pre-existing trade-unions, or the use of social networks (virtual or not), and that is a matter of algorithmic nature, on which I claim no informed knowledge. In any case, coordination in game theory assumes the existence of a benevolent referee which Tunisia and Egypt proved to be non-existent or negligible.

The whole exercise is pointless, save perhaps the idea that revolutions are not inherently dysfunctional occurrences of otherwise rational institutions and behaviour. With a bit of game theory, it can be proven that it is fully rational, and that the only problems in completing the argument are not related to reason, and could nonetheless be expected with the help of otherwise more randomized experiences.

The Good, The Bad, The Ugly & The Game Theory

Posted in Dismal Economics, Read & Heard, The Wanderer by Zouhair ABH on February 2, 2011

Though weather is manageable, I caught a cold. Not worrying, but I might be needing a rest, at a moment I need it the least: Game Theory is getting stiff: The conditions for a strategy-proof monetary policy are trickier than assumed, but hey, I shall be posting on that very shortly.

I was just rewatching “The Good The Bad & The Ugly” by Sergio Leone. There are movies that one can never get enough of watching over and over again, and Leone’s tetralogy are no exception. I particularly like the last scene, where Tuco (Ellie Walach), Angel/Sentenza (Lee Van Cliff) and Blondie (Clint Eastwood) compete remorselessly for a treasure left by confederate troops.

The scene I am referring to is the final duel, when the three protagonists face each other, and set on killing for the confederate gold worth $ 200,000. Actually, I was listening to the movie while working on Osborne’s ‘Game Theory’ (I know, it is not much productive, but there are bad habits one enjoys thoroughly) I could not help myself but to link both things: isn’t the final scene a good illustration for game theory? Since many of my friends advised me to write lighter pieces, I shall use this one as an experiment: how to do some game theory with Sergio Leone (and your humble servant too)

There are three duellers: The Good (Blondie), The Bad (Sentenza) and the Ugly (Tuco). They compete for a certain amount of money ($ 200,000), hidden in a certain tomb, whose name’s Blondie (the Good) wrote on a piece of rock. In essence, all players are equal, due to the fact that they have the same amount of ammunition, and when they shoot, they cannot fire quickly enough and kill the two others! If they do draw, it’s against one and only one other dueller, and so, there is no possibility for collusion (as in: ‘Blondie, let’s get rid of this pig Angel!’ or ‘Tuco, you’re a good man, you should get some bucks out of Blondie’s corpse.’)

These conditions reduce the game to a basic form: which opponent each dueller is going to shoot? Payoffs are also pretty clear: the player either gets money or gets killed. Is there equilibrium here? In layman’s terms, is there a situation whereby duellers get the money and do not change their mind if they are offered to re-do the duel?

Clint Eastwood's rendition of Blondie was terrific. So was he in the other movies.

In fact, it seems there is. Not because the movie suggests so (as it later turns out, Blondie had Tuco’s pistol emptied the night before they reached the cemetery. In that sense, Blondie had a strictly dominant strategy of shooting Sentenza, which he did) but because the whole structure of the game incentive each dueller to implicitly coordinate with another to bring down the third: regardless of Blondie’s trick, both Blondie and Tuco fired –or tried to- on Angel. Why so, and was it equilibrium? If it was to be done again, would one of them at least change their mind?

Now, the game is imperfect: all three duellers have a history together. They know that of the three, Angel is the most ruthless and no one benefits from allying with him. On the other hand, Blondie and Tuco have a history of lucrative cooperation.

The table shows clearly that is it better to team up with with someone against the third dueller, rather than just draw and shoot at random (payoffs are sufficiently clear for them not to randomize. In gibberish economics, that means there’s already a Nash equilibrium, so randomizing is not necessary – the outcome of Nash equilibrium is obtained by mixed strategies). We need however, to introduce another condition: because all three protagonists dealt with each other before, they have preferences over their respective ‘partner’. It is reasonable to consider their preferences as follows:

For Tuco: U>G>B
For Blondie: G>U>B
For Sentenza: B>U>G

(note: duellers are considered selfish, so they prefer to take all the bounty to themselves, then choose another protagonist when needs to be) Because of that ordering, and even though pay-offs are the same when teaming-up occurs, both Blondie and Tuco have incentive to cooperate and shoot Sentenza, which eventually happened. In essence, there was little high-brow rationality, especially for Tuco: he is the exclusive second choice of both duellers, and he is better off with Blondie than he is with Sentenza -per his own preferences-.

Why does it constitute an equilibrium? Because it dominates all other moves, i.e. duellers -at least Blondie and Tuco- are better off and do not want to wish to change from their choices: Blondie prefers to split the money with Tuco, and so does the latter. Sentenza is know to be ruthless and has every incentive to keep it that way. It is thus a stable equilibrium.

Afrinomad put to me this proposal: can we find some Game Theory application to the current wave of revolutionary fervour in the MENA region? I must confess I got very enthusiastic over this idea: however intermediate my knowledge in game theory is, I’d very much like to give it a shot. So I would like to post on my own terms: ‘are the people of MENA ready to throw over their rulers, under Game Theory settings?’. Stay Tuned!