Monday, December 16, 2013

A Game of Institutions Book 1: Euvoluntary Coordination

I beg your indulgence for a brief series of posts. In them, I shall expand on the Shughart/Thomas piece, discussed here. Casual readers can think of this as a brief introduction to elementary game theory. For my more knowledgeable readers, think of this as some preliminary spitballing prior to an actual project.

Before I get to the specifics, I'll need to walk you through the basics of practical game theory. I apologize if this is old hat—please feel free to skip ahead if you like.

First off, the Twitter version of game theory. It's a way to analyze strategic behavior. That's it. Nothing fancy. There are three basic elements to any game: players, payouts, and choices. Most instructors will start out with 2-player games to illustrate the mechanics of finding an equilibrium solution, since it helps students moisten their feet without the risk of drowning. We can do the same here, but discussing constitutions necessarily implies more than just 2 players. Getting there will be easier if we start with the simplest case first: euvoluntary constitutions and the Coordination Game.

A (sequential) two-player CG goes a little a-something a-like this. P1 chooses to play left (L) or right (R). P2 then also chooses to play L or R. If both players play L, each earns 10. If both players play R, each earns 5. If either one plays L and the other plays R, each earn 0. Here's the payoff matrix, with P1 and P2 payoffs separated by a comma:


The actual amounts in the cells are for illustration only. What's important here is the symmetry: P1 and P2 are equally better off by picking the same choice than by accepting their BATNA. And worthy of note for euvoluntary exchange purposes, their BATNAs are identical (nb: I know that the proper parlance would be "Best Alternative To a Coordinated Outcome, but let's just stick with our tried-and-true acronym). With symmetrical payoffs, none of the players' sense of fairness or justice is offended. We work together to produce something, then split the proceeds even-Steven.

What's the point then of a constitution? In a sequential game, I pick L, then you pick L, we're good to go. Equilibrium outcome, hooray (and yes, [R,R] is also an equilibrium outcome)! Well, if we're playing a repeated simultaneous game, it'd be nice to know beforehand what the expectations are for play. Think of it as a preliminary cheap-talk round. I say "left" you say "cool" and off we go. Recall from S&T that a euvoluntary constitution is one that does not require ex post enforcement to remain valid. This qualifies. There's no upside, no incentive to play anything but the agreed-upon action.

To make this game more interesting, you can include more players, discount rates, production functions, and whatever other bells and whistles you might like. But the core observation that no coercion is needed to reinforce the terms of the constitution remains so long as we've got symmetrical payoffs and a barren BATNA.

So what are some real-world analogs to this coordination game? Well, partnerships come to mind. Think about the default legal rules for a partnership: there's joint and several legal liability, but more to the point, any of the partners can dissolve the partnership at any time for any (or no) reason whatsoever. This is an attractive feature for firms wishing to signal euvoluntarity.

Consider this, then. Marriage, under no-fault divorce, is closer to the default rules for partnership than it was under a statutory harm regime. That is to say that the rules for divorce we have now are more euvoluntary than they were prior to 1969. If you believe Wolfers and Stevenson (and you should, their econometrics are impeccable), domestic violence rates and suicide dropped precipitously because of no-fault divorce, with no long-term impact on overall divorce rates (yes, there was a spike at the time of the regime change, but you can think of that as pent-up demand). But what if the more-euvoluntary institutional rules were in fact unfit for marriage? Marriage rates in the US began to tank in the 1970s, and the median age of first-time married couples has risen (CDC and Census). If you believe Charles Murray, these trends rend asunder the tissue paper of society. Let's ditch the normative assumptions and take at face value both the Wolfers/Stevenson claims and the Murray conclusion. Is it possible then to have an increasingly euvoluntary institution that produces decreasingly euvoluntary outcomes? Another way to think about this is whether or not we can have instances of private goods that add up in a separating equilibrium to a public bad.

If that smells a little bit like a false dichotomy, it's because it probably is. There are other ways to discourage single parenthood (on the margin, naturally) while preserving liberal freedom of association. Reconsidering the move away from virtue ethics towards Kantian moral imperatives or naked utilitarianism might be a good place to start. Aspirational sentiments in fiction might be another. Solving great social problems is off-topic here, I merely wish you to consider if Simpson's Paradox need apply to institutional choice, and if it does, what are the implications for default rules?

Okay, so I didn't get all that heavy into the game theory in this post. For forthcoming posts in this series (under the 'S&T' tag), I'll make things a little bit more rigorous. I'd like to get to where we're estimating comparative statics for an n-player game, including terms for fairness preferences. I hope to convince you that this approach can help explain why we see the sorts of big institutions we have, and if I do my job right, that both Locke and Rousseau can be correct about the origins of the state.

Sounds fun, doesn't it?

No comments:

Post a Comment

Do you have suggestions on where we could find more examples of this phenomenon?