## Friday, December 20, 2013

### The Importance of Screening

In my first new post, I articulated one way international institutions can deter bad behavior. In this post, I'll argue that even if we assume institutions don't have access to information that isn't already available to states, they still matter more than some appreciate.$$^1$$

One of the most prominent criticisms of institutions is that they are epiphenomenal---that they put a name on behavior that would have occurred anyway. That is, some have argued that the good news about compliance is not necessarily good news about cooperation because treaties may simply screen rather than constrain.

But the one does not necessarily imply the other. That is, even if institutions merely screen without constraining, this may nonetheless give us cause to celebrate international institutions. Below, I discuss a result from a formal model in which institutions screen but do not constrain---a model where the willingness of any given state to comply with a cooperative outcome is the same regardless of whether they join the institution. But it is nonetheless true in this model that fewer states would cooperate in the absence of institutions. In other words, when assessing the impact of institutions, we have to be very clear about what our standards are (as Martin and others (1 and 2) have argued). There is an important distinction between the claim that institutions alter state preferences and the claim that they merely separate nice, trustworthy types from bad, untrustworthy types, and I do not wish to downplay it. But it is nonetheless true that screening matters.

Brief Synopsis

Yes, the problem of international cooperation is sometimes one of incompatible interests. But there is good reason to believe that money is sometimes left lying on the ground due to a variety of factors. One is a lack of trust. As I will demonstrate below (and as others have proven before), it is possible for two trustworthy states to fail to cooperate with one another due to their inability to credibly convince one another that they are trustworthy. If institutions screen (and they must at least do that---remember, this is a debate about how to interpret the empirical regularity linking membership in institutions to higher levels of cooperation, not whether such a correlation exists) that necessarily means that they help solve the information problem that we have cause to believe might otherwise inhibit cooperation.

In other words, the most prominent critique of international institutions holds that they do not alter the behavior of bad states. That may or may not be true, but even if it is, this nonetheless implies that a world without institutions would likely be a world with less cooperation. The debate about whether institutions constrain or screen is not a debate about whether institutions matter for international cooperation. It's a debate about precisely how they go about increasing cooperation, and amongst which subset of states.

Details of the Argument

Suppose we have two states, denoted 1 and 2. At the start of the game, 1 chooses whether to present a written agreement to 2 or not, incurring cost $$\kappa_1 \in (0,1]$$ if she does so. 2 then decides whether to add her signature. Doing so requires her to pay cost $$\kappa_2 \in (0,1]$$.

Regardless of what happens in the first stage, the two then play a normal form subgame. I stress that the payoffs from the subgame are not in any way affected by whether 1 presented an agreement to 2, or whether 2 signed the agreement in the event that one was presented. That is, agreements do not affect the value of mutual cooperation relative any other outcome.$$^2$$ In other words, I assume for the sake of argument that institutions have no power whatsoever to constrain state behavior.

In the subgame, each state chooses whether to cooperate or not. If and only if both states cooperate, the outcome is mutual cooperation.$$^3$$ This brings 1 a benefit of $$\beta_1$$ and 2 a benefit of $$\beta_2$$. More on that below.

If state $$i$$ chooses not to cooperate while $$j$$ does not, where $$i \in \{1,2\}, j \in \{1,2\}$$ and $$i \neq j$$, then $$i$$ receives a temptation payoff worth $$\tau_i$$ while $$j$$ receives 0.

If neither state chooses to cooperate, each simply receives their status quo payoff, which is assumed to be worth $$q \in (0,min\{\color{red}{\underline{\beta}_1}, \color{red}{\underline{\beta}_2}\})$$.$$^4$$

Each player is uncertain about their opponent's type. But $$i$$ knows that $$pr(\beta_j=\color{blue}{\overline{\beta}_j}) = \color{blue}{\phi_j}$$ and $$pr(\beta_j=\color{red}{\underline{\beta}_j}) = \color{red}{1-\phi_j}$$, where $$0 < \color{red}{\underline{\beta}_j} < \tau < \color{blue}{\overline{\beta}_j}$$. That is, each player knows that there is some chance that their opponent is the nice, blue type, who prefers mutual cooperation to all other outcomes, and some chance that they are the mean, red type, who agrees that mutual cooperation is preferable to the status quo but nonetheless finds the temptation payoff more attractive than the benefits of mutual cooperation.

Note that this specification is quite flexible. The Prisoner's Dilemma is a special case of this subgame, as is the Stag Hunt.

I won't go through a full analysis of the game. But I will sketch a proof of the existence of a perfect Bayesian equilibrium where 1 and 2 achieve mutual cooperation provided that both are blue types but would have failed to do so if we removed the option of international agreements.

First, suppose that $$\color{blue}{\phi_1} < \color{blue}{\overline{\phi}_1}$$ and $$\color{blue}{\phi_2} < \color{blue}{\overline{\phi}_2}$$, where $$\color{blue}{\overline{\phi}_j} \equiv \displaystyle \frac{q}{\color{blue}{\overline{\beta}_i} + q - \tau_i}$$. That is, $$\color{blue}{\overline{\phi}_j}$$ is the minimum level of trust in $$j$$ that the blue type if $$i$$ must have before $$i$$ is willing to attempt cooperation, and we're going to focus on situations where the initial level of trust 1 has in 2 and the initial level of trust 2 has in 1 both fail to meet their respective thresholds. In such cases, the status quo will prevail and money will be left lying on the floor even if both states are the good, trustworthy blue types.

Can institutions get us to a happier place?

Well, if the answer wasn't yes, I wouldn't be writing this post. But bear with me. Provided that $$\color{red}{\underline{\beta}_i} < \kappa_i < \color{blue}{\overline{\beta}_i}$$ for both players, then 1 presents an agreement to 2 if and only if 1 is blue, and 2 signs that agreement if and if 2 is blue, and both players pursue cooperation in the subgame if and only if they are blue. Thus, provided that both players are indeed blue, mutual cooperation will occur as a result of an international agreement that screened out red types yet which had no power to constrain the behavior anyone. Recall, as specified above, this outcome would not obtain absent the agreement.

How big does $$\kappa$$ need to be for this argument to work? Actually, not very big at all, provided we believe that some states don't ascribe much value to mutual cooperation. That is, as $$\color{red}{\underline{\beta}_i} \rightarrow 0$$, the values of $$\kappa$$ for which this argument works also go to 0. In other words, the more seriously you take the possibility that states do not always have a harmony of interest, the less grounds for skepticism you have about the potential benefits of international institutions.

Well, okay, that's not entirely fair. As $$\color{blue}{\overline{\beta}_i} \rightarrow 0$$, the range of values of $$\kappa$$ for which the argument works shrinks. So what I really should say is that offensive realists, who believe states pretty much always view one another as extreme threats, can safely dismiss this argument without contradicting themselves. But the same cannot be said of those who believe that some states are less aggressive than others yet who doubt the ability of states to credibly communicate their trustworthiness, which I'm pretty sure includes a number of scholars who are unduly skeptical about the role of international institutions. If you think the international system is a relatively dangerous place, but not one that promotes hyper-insecurity, it would be reasonable for you to question the extent to which international institutions constrain state behavior, reigning in those who would otherwise be inclined to misbehave, but it you have little basis for claiming that international institutions don't matter. Institutions need not constrain in order to facilitate cooperation that would not otherwise occur. Screening alone is a pretty big deal.

1. Rest assured, this blog has not shifted its primary focus from conflict to cooperation. I've been thinking more about the latter lately because I've been teaching intro to international relations a lot lately and I try not to focus too heavily in that class on my particular research interests. But I haven't lost my unhealthy preoccupation with dead bodies and the production thereof.

2. They may affect players' expected utilities from pursuing a strategy of cooperation, however. And of course, that's important. But the outcomes themselves are unaffected.

3. You'd think this point so obvious as to hardly be worth stating, but classroom experience convinces me otherwise.

4. We don't need to assume that the players attach equal value to both mutual cooperation and the status quo, but it simplifies the analysis considerably, so roll with me.

1. Footnote #1 is reassuring.

2. It is nice to see even you conflict people acknowledging how important cooperation is ;)

1. Took me a while, but I came around. :)

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