Legal philosophers: please don't talk about coordination games any more

UPDATE, July 7th, see below.

---

Despite Les Green's best efforts (The Authority of the State, "Law, Coordination, and the Common Good"), this seems to be one of those inapt metaphors that just won't die. Some scattered thoughts on the use and misuse of game-theoretic "coordination games" in analyzing the normativity of laws or legal orders generally.

1. If game theory is to illuminate rather than obscure, practitioners must be clear about the players, strategy and information sets, and payoffs. They must show why this game (as opposed to slightly-modified versions that induce with different equilibria) is appropriate for understanding the real-world phenomenon in question. I almost never see this.

2. If the point of the model is to show why we should expect an exogenously imposed change in payoffs, or elimination/addition of strategies--in other words, explaining exogenous law, or the exogenous creation of an entire legal order--the shift cannot be a deus ex machina. What is the mechanism that leads from the original equilibrium to the imposition of sanctions or what-have-you? Who are the players that impose the sanctions; why and how do they do so?

3. Modeling constitutional choice is easy to do badly. It is rarely appropriate to model strategy sets as consisting of regime types. You can't "play" a regime; one emerges as the institutional embodiment of the intersecting strategies of others. If you're at a constitutional convention, you can vote for a regime type, but determining how votes translate into outcomes and payoffs is very tricky and entails hard counterfactuals. When does a vote of X induce factional violence, as opposed to multiple polities, as opposed to some uneasy status quo ante? If instead you wish to model a "state of nature" situation, there is no good reason to include private violence as within the strategy set but not include the violence of players constituting a state.

4. Once we allow for the full set of strategies--and violence--open to players in a state of nature situation, it is obvious that many equilibria will be awful, much worse than many non-equilibrium outcomes. Some equilibria will look like states, some will not. Some will have normatively desirable properties. Outcomes that describe a voluntarist legal order--no sanctions--are unlikely to be equilibria, which is a basic reason states reach for sanctions. Insofar as this model is supposed to explain the emergence of states, it will emphasize the importance of bargaining power, contingency, and path dependence, rather than justice or welfare.

5. Similarly, looking at ongoing polities as large-N games is unlikely to help legitimate the state. A full accounting of strategies and outcomes is likely to once again highlight contingency, power, and path dependence: the incentives that induce the players to go along with the state are rarely as stark or systemic as "my choice brings about system X." Individual sanctioning, rather than the collapse of the polity, generally does the work. This is old stuff, Hume and earlier.

6. None of this is to deny that citizens often do consider their governments legitimate, nor to deny that these beliefs often track (perceptions of) procedural, systemic properties rather than personal advantage. It is merely to note the ceteris paribus importance of state coercion.

7. The bottom line: if coordination game means something more stringent than "multiple equilibria which are local maxima for almost everyone"--in particular, if it means "multiple equilibria, each of which pareto-dominates non-equilibrium outcomes"--there is no reason to think it applies either to state-of-nature anarchy situations or to ongoing regime resist-or-support situations. But if we weaken it to the former definition, then the fact that a particular outcome is an equilibrium carries no normative weight beyond surmounting the "ought implies can" barrier. It is therefore misleading to use a term that carries such significant connotations of mutual advantage, both in game theory and in ordinary language.

8. And also: insofar as coordination games are taken to mean games where everyone plays "corresponding" or "matching" strategies in the multiple equilibria, it's just not clear how the idea of "correspondence" adds anything meaningful in the context of constitutional order and maintenance. It is a property of the emergent outcome, rather than the strategy of an agent considered alone, that makes a certain series of actions come under the description "following the constitution of polity X" rather than "disobeying Y" or "fighting for Z." Claiming that *only* outcomes like the first are equilibria is false to the reality of order's fragility and the diversity of human interests. Is the civil war in Iraq supposed to represent "matching" strategies among factions? If so, the idea of "coordination" adds nothing to that of equilibrium simpliciter; if not, then it's not generally applicable to questions of order.

Blah!

UPDATE: Just so clarify a bit, I'm not saying game theory can never be useful in legal philosophy; it can. I'm not even saying coordination games are never apt; Gerald Postema's "Coordination and Convention at the Foundations of Law," J. Legal Studies 1982, is perhaps the best example of it done right. My point is rather that there are so many ways of going wrong, so many traps that seem to catch even those who surely know better, that it should be used only as a last resort, and then with fear and trembling.