HowTo: The Prisoner’s Dilemma. Or, strikes are neither good nor bad economics. Just economics.

This has been bothering me since I saw it (which is to say, since I began to have no time for anything but dealing with exams and looking up Mos Def clips on Youtube – what?).

From the Huffington Post, sometime during the weekend (just prior to the writers’ strike).

… the representatives of the Writers Guild have to remember is that all union contract negotiations are to set minimums, and that the effect of the change in residuals from DVDs and New Media they are seeking will not rise to the level of revenue they are asking for – or what the strike is going to cost the Guild’s active members. Once again, the eventual cost of a strike will exceed the financial gain being sought.

Going on strike to lose more than you gain is not smart negotiating.

The writer (Ari Emanuel) is making more than just this point, but this point is still his central one, and it betrays a lack of understanding of at least game theory.

Simultaneous Games

Let’s simplify the game a bit. Two players (writers and studios, i.e. a Duopoly) are bargaining for revenue (the payoff). They can co-operate or not co-operate (writers can strike or not strike; studios can pay the writers demands or not pay). This gives us the Prisoner’s Dilemma, and the following payoff matrix:

Payoff matrix 1

Or does it? In Payoff Matrix 1 (before-the-comma = Writers, after-the-comma = Studios), I’m suggesting more-or-less a zero-sum game, working from the status quo (i.e. revenues are re-distributed). Each player’s Dominant Strategy varies: Studios should not co-operate, but writers should – i.e. striking is, as Ari Emanuel suggests, a bad move (but not, I would remind you, bad economics – we’re having fun, right?). This is following his suggestion that they lose more than they gain (reflected in the payoffs). Striking is not the Nash Equilibrium.

Suppose instead that the payoff to co-operation includes some compromise, but ‘winning’ by non-co-operation secures higher payoff (since you then do not need to compromise – Gingrich revolution, anyone?). Then we’d have another imaginary payoff matrix, such as:

Payoff Matrix 2

Here the Dominant Strategies converge to the classic Nash Equilibria of non-co-operation, and it’s perfectly sensible, since these are as the Dominant Strategies dictate (the Dominant Strategy is the one that has the highest payoff, irrespective of what the other player does).

The real lesson, I hope you saw, was that that we don’t really know the payoffs, and changing the payoffs changes everything. Clearly the writers believe that non-co-operation will benefit them. The other lesson is that we should be careful about dealing with this as a simultaneous game.

Sequential Games

Suppose that, rather than this paper-rock-scissors-simultaneity, the Guild of whomever and the studios bargain in an ongoing game, of which this is one episode. There is no Nash Equilibrium needed, necessarily, because repeated games inter-act (or, at least, their players do).

This then generates the real question: to what end does this strike tend? Is it designed to secure a higher payoff than co-operation in this game? Or is it designed to secure higher payoffs in future games? My thoughts are that it is more likely to be the latter.

The key to a good bluff, after all, is that, sometimes, you do need to be holding all the cards (Bernanke could do with being reminded of this, for example – if you can tear him away from cutting interest rates everytime he gets 4 other people into a room).

This, then, makes the writers’ strike an excellent game-theoretic move. Studios need to be reminded that there is punishment for repeated non-co-operation (remember, their Dominant Strategy was non-co-operation, so they will do that always) – periodically they will need to be punished for this. Every such player in every such repeated game needs such a reminder (Democrats might do with being reminded of this fact, if they can remember where they stashed away their backbones, back in ’95).

So, to Ari Emanuel’s claim that political posturing is going to interfere with good economics (question mark): the posturing – political or not – is part of the economics. He also closes his argument with calling for consideration of everybody else affected:

… not only for the sake of the writers, the studios, and the networks but for the millions of people in the community who will be hurt by a strike, including below-the-line workers and all those who aren’t in show business but whose livelihood is dependent on a Hollywood that is up and running.

That is, sad to say, bad economics. None of those people were in the game, for a good reason: they are not in the game. The writers’ guild is not responsible for the outcomes to non-writers. If those players want to participate, they ought to form collective representation and make the writers another offer not to strike – i.e. compensate the writers themselves, for the losses they will incur by leaving the studios to take advantage of them (again). Or compensate the studios for co-operating.

Something, though. The Dominant Strategies are the Dominant Strategies, and anyone trying to overcome those on behalf of negative externalities needs to come up with compensation to shift those Dominant Strategies to ones without negative externalities (the Coasean solution to negative externalities in repeated games – I think I just earned my Nobel prize).

The Agency Problem

A final problem, not addressed in the article, but still relevant with unions and industrial action. Consider the following:

Who strikes? The union.

Why? To secure better outcomes for the members of the union.

Really? Not necessarily, no.

What does the Union have to gain? More than just good outcomes for its members. What does the GOP have to gain from rail-roading Congress and the Senate away from a properly-functioning house of democracy? The people lose, but the GOP looks tough for its members – who re-elect them, support them, etc.

Unions can push a strike earlier than when a strike is deemed to be properly necessarily. They can push – and maintain – a strike when, in a repeated game, they come to be perceived as weak. This is the agency problem: the union telling you that you need to strike is the same one that will sell it to you.

We don’t like to think this way (I don’t – I’m Australian, for Cliff’s sake). However, we also do not like to think this way about doctor’s, dentists, lawyers (maybe not lawyers), politicians – the list goes on and on. Climate change scientists. Engineers. Why not unions?

This is, I should say, also neither good nor bad economics – just economics. People work according to their own self-interests. We assume unions push a strike because their self-interest accord with those of their members (like government, like the medical profession, like the sciences); there’s no reason why this always has to be the case, though. If their self-interests diverge, the Union, as an economic agent, will still operate in its own self-interest.

So: strikes. Neither good economics, nor bad. Just economics.


1 comment so far

  1. Maira on

    Good. I agree.

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