Tuesday, 24 April 2012

Game Theory & The Occupy Movement


Game Theory & The Occupy Movement

The global Occupy Movement in its current incarnation can be characterised quite accurately in terms of a War of Attrition, to use evolutionary game theoretic terms.

At the starting point of evolutionary game theory, the first game analysed by Maynard Smiths was called Hawk and Dove. In this game, two contestants vie over a sharable resource. The two correspondent strategies are that of Hawk and Dove. To play the Hawk is to display aggressive behaviours, then escalate the competition for the resource until either the Hawk wins or else is injured. Dove’s strategy in the game is to first make a show of aggression, but, when faced with escalation to physical violence, will turn heel and run away.

Here is the payoff matrix for the Hawk / Dove game:

So, War of Attrition — cool name, right? War of Attrition is identical to the Hawk and Dove scenario, albeit that the resource is deemed unsharable. So in the above scenario where either two Hawks or two Doves vie, the desired resource is divided in accordance with the payoff matrix. But in War of Attrition, this sharing or splitting of resources is no longer an option, and so the violently aggressive behaviours associated with the Hawk / Dove game are no longer effective strategies. Instead, in War of Attrition, two new strategies, known as Bluffer and Bourgeois emerge:

A safer strategy of display, bluffing and waiting to win, then becomes viable – a Bluffer strategy. The game then becomes one of accumulating costs, either the costs of displaying or costs of prolonged unresolved engagement. It’s effectively an auction; the winner is the contestant who will swallow the greater cost while the loser gets, for all his pains, the same cost as the winner but NO resource. The resulting evolutionary game theory mathematics leads to an optimal strategy of timed bluffing, where any player backs off with equal probability at any time in the contest – unguessable by his opponent. This is exactly what is observed in nature for contests in a number of species, for example between male dung flies contesting for mating sites. The timing of disengagement in these contests follows the exact mathematical curve derived from the evolutionary theory mathematics.

There is a mutant strategy which can better that of Bluffer in the War of Attrition Game. This is the Bourgeois strategy (Maynard Smith named the strategy Bourgeois, because with his background of communism he regarded it as “politically bourgeois” way to value ownership). Bourgeois uses an asymmetry of some sort to break the deadlock. In nature one such asymmetry is possession – which contestant has the prior possession of the resource. The strategy is to play a Hawk if in possession of the resource, but to display then retreat if not in possession.

If one takes a look at the Collusive and Nash Equilibriums for the War of Attrition, it is clear that costs are exorbitantly high to both players involved. However, payoff in terms of resources in this game is always maximized for the Collusive Equilibrium.

I realise that last paragraph might be gobbledegook to some. Basically, what this means is that if both people stand around bluffing for a long time, or, even worse, if one just sits on an unshared resource and the other one randomly runs up and puts on a show of dissent or aggression, nothing’s going to get done. There will be high costs to both parties in the long run. It would be better for the two parties to collude and thus share the “unsharable” resource.

As for the Occupy Movement, I think you understand where I’m going. We have a class of bourgeois dining on balconies and drinking champagne, while staring down at a bunch of rabble-rousing protesters with tents on Wall St. We have one group who is sitting smugly on a pile of ill-used resources, and another group who is quite literally putting on a show of aggression for the former. Now, the occupation is non-violent, we all know this. And thus, the former group knows that this show is a bluff. Nothing will happen. They can sit there drinking their champagne all day, and nothing is going to change.

Hey, Occupiers! Guess what?

Bluffing is not an effective strategy.


This was written by Isis. Posted on Saturday, October 22, 2011, at 0054. Filed under Game Theory. Tagged ,. Bookmark the permalink. Follow comments here with the RSS feed. Both comments and trackbacks are currently closed.

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