Game Theory & Revolutions
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
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.