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Domestic institutions and international bargaining: the role of agent veto in two-level games.

According to Putnam (1988), two-level games characterize situations in which a negotiator finds herself simultaneously engaging in both domestic and international bargaining. Domestic bargaining is necessary because an international agreement is usually subject to ratification. This requirement constitutes a negotiator's domestic constraint, limiting the range of proposals that the negotiator can accept. Putnam shows that a negotiator can actually strike a better bargain when she is subject to such a domestic constraint; the negotiator can use the hardline position of her domestic constituent to extract more concessions from a foreign country.(1)

I shall take Putnam's argument one step further and ask whether a negotiator will actually prefer to impose a domestic constraint on herself by granting veto power to her domestic constituent. If a domestic constraint is as beneficial as Putnam suggests, the negotiator will certainly want to have it as a bargaining tool. More broadly, I shall use Putnam's model of two-level games to address the issue of institutional design in international negotiation theory. If ratification procedures affect international bargaining outcome with significant distributive consequences among domestic actors, it is unreasonable to think that ratification procedures are exogenously given (Evans 1993, 415; Pahre 1994). Those domestic actors with stakes in international bargaining outcome have an incentive to choose a domestic bargaining institution favorable to their interests. Although Putnam suggests that an international negotiator has such an incentive, the conditions under which she will actually give veto power to another domestic actor have not been derived.(2)

In the model presented, there are two domestic actors, a principal and an agent.(3) The principal as the negotiator is assumed to have the power to design a ratification procedure (i.e., whether to give veto power to an agent). Unlike Putnam, I do not restrict the principal-agent relationship in my model to the executive-legislative conflict. The agent in the model does not have to be a legislature; it can be an interest group, an executive branch agency, or a congressional committee that can exercise de facto veto power over an international agreement. Likewise, the negotiator in the model does not have to be a chief of government. In the case of trade policymaking in the United States, it is more reasonable to think of Congress as the principal and the president as her agent because Congress with its constitutional authority can design trade policy institutions and shape trade negotiations.

The agent, if given veto power, can approve or reject an agreement that has been negotiated with a foreign country. Since the only source of domestic player's bargaining power in the model is their veto power, the agent plays no role in the game without the agent veto. This model best captures Putnam's logic of two-level games in which international bargaining is dominated by the negotiator's search for ratifiable agreements.

If the agent is given veto power, the foreign country must make a proposal acceptable not only to the principal but also to her agent. As Putnam suggests, this new constraint may benefit the principal by forcing the foreign country to make more concessions. In fact, I will show that when the foreign country has complete information on the principal's preferences, it is always better for the principal to grant veto power to the agent.

If the foreign country has incomplete information about the principal's preferences, the principal's incentive to use the agent veto weakens; it now depends on the closeness of the preferences between the principal and the agent. However, even in this case the principal's incentive to use the agent veto remains strong in the sense that the principal avoids the agent veto only if her agent has interests very divergent from the principal's own. The principal's preference for the agent veto is in large part due to its informational effect, an element not considered by Schelling and Putnam. That is, the use of the agent veto affects the way information is transmitted during the negotiation.

Since the foreign country must seek the agreement of the agent with veto power, it may propose an outcome too far from the principal's ideal outcome. In that case, some types of the principal will reveal their true type to induce the foreign country to make a proposal closer to their ideal outcome. In other words, if an agent with veto power has an extreme position against the foreign country, moderate types of principal will reveal their true preferences instead of trying to bluff the foreign country. If they bluff, they know that the foreign country will make a proposal too close to an agent's position, so they do not have an incentive to bluff. Without the agent veto, however, the principal cannot credibly send information to the foreign country because the principal cannot credibly commit herself to not bluffing. Thus, when the agent has veto power, the principal is able to transmit information to the foreign country and capture informational gains that would be lost in the absence of the agent veto.

The agent's veto power, however, imposes costs on the principal. The principal suffers distributive losses when the agent's veto power forces the foreign country to make a proposal close to the agent's ideal outcome. Therefore, in choosing to grant veto power to the agent, the principal faces a trade-off between informational gains and distributive losses. How the principal resolves this trade-off depends on the alignment of preferences between herself and the agent. If the ideal outcomes of the principal and the agent are relatively close, the principal will use the agent veto; otherwise, the agent does not receive veto authority.

THE MODEL

A principal (P) and an agent (A) representing one country bargain with a foreign country (F) to determine a policy outcome x [element of] X where X is assumed to be the unit interval. The status quo or disagreement outcome q in X is 0. The players' preferences in X are assumed to be single-peaked with an ideal point. To simplify the analysis, I further assume that their utility functions are quadratic and symmetric around their ideal point and are represented as

[u.sub.p] = -[(x - [x.sub.p]).sup.2],

[u.sub.a] = -[(x - [x.sub.a]).sup.2],

[u.sub.f] = -[(x - [x.sub.f]).sup.2],

where [x.sub.p], [x.sub.a] and [x.sub.f] are P, A, and F's ideal points in X, respectively. I assume [x.sub.f] = 1, indicating that F is least satisfied with q. I also assume that both P and A prefer some deal to the status quo; that is, [x.sub.p], [x.sub.a] [greater than] 0. Otherwise, A can obstruct the negotiation by rejecting any agreement greater than q, and P has no incentive to employ such an agent. P and A's preferences over policies with respect to q are illustrated in Figure 1.

The information structure of the model is as follows. F has incomplete information on P's preferences, that is, [x.sub.p].(4) Negotiators do not have precise information on the preferences of their foreign counterparts and are placed in a position of "figuring out" what they want. But F is assumed to have complete information on A's preferences. Unlike the principal who, as the negotiator, has to represent a diverse group of domestic interests, the agent is assumed to represent a much narrower domestic interest and thus to have relatively well known preferences; that is, the agent has established its reputation as a hawk, a dove, or a moderate.

In order to facilitate the exposition, P's type, t, will be assumed to represent not its ideal point [x.sub.p] but the outcome 2[x.sub.p] that gives the same utility to P as the status quo, q. The set of P's types is T = [[t.sub.1], [t.sub.h]], and this means that P's ideal points are distributed over [[t.sub.l]/2, [t.sub.h]/2].

This parameterization identifies the set of points that P prefers to q. For type t, this set is [0, t]. In order to preclude situations in which P favors F's ideal point over q, we assume that [t.sub.h] [less than] 1. Similarly, the set of points that A prefers to q is [0, 2[x.sub.a]], and 2[x.sub.a] [less than] 1. It is highly unlikely that domestic actors favor a foreign country's ideal outcome over the status quo.

P's types are drawn from a density function f([center dot]) over the interval [[t.sub.l], [t.sub.h]]. This density function f([center dot]) is common knowledge but, as noted, the realization of t is private information to P.

The game follows a sequence of moves as illustrated in Figure 2. At the initial regime choice stage, P chooses the agent-veto or unitary regime, depending on whether P grants veto power to A. After P chooses a regime, P's type is revealed to p.(5) P is assumed to choose a bargaining regime before it knows its future preferences with certainty because a bargaining regime or institution, once created, is difficult to change, especially in international negotiations. For example, although P may anticipate that her preferences over trade policy shift as a result of change in economic conditions, it will be too costly to revise trade laws or institutions simply as a function of economic conditions. P, however, has expectations about her future type t which coincides with those of F; that is, t [similar to] U[[t.sub.l], [t.sub.h]].

Once a regime is chosen and private information is revealed, P and F play a three-stage bargaining game similar to that of Matthews (1989). At the rhetoric stage, P sends a message about t to F. F responds to it by proposing a policy x at the proposal stage. At the approval stage P and A (if given veto power) accept or reject x. If the proposal is rejected by either player, the final outcome is the status quo, q.

For each type t [element of] T of P, P's pure strategy signal rule is m:T [approaches] S, where s = m(t) is the message sent by P of type t and S [equivalent to] T is the set of messages.(6) F's strategy set at the proposal stage is the set of all pure strategy proposal rules mapping messages into proposals: [Pi]:S [approaches] X.

P's acceptance rule at the approval stage is a function [[Alpha].sub.p],(x, t):X [approaches] {0, 1}, which takes a value 1 if a P of type t accepts proposal x and 0, otherwise. A's acceptance rule [[Alpha].sub.a](x):X [approaches] {0, 1} is similarly defined.

There are many Nash equilibria in this game. I use the concept of sequential equilibrium to focus on a reasonable equilibrium. A sequential equilibrium requires four things:

1. At the approval stages, both P and A (if A is given veto power) never reject a proposal that they (weakly) prefer to the status quo; otherwise, their strategies are not subgame perfect. That is, they cannot commit to act in a manner not in their interests at the approval stage.

2. P sends a message to induce its most preferred proposal, given F's equilibrium proposal strategy.

3. F's updated beliefs are consistent with P's optimal signaling strategy.

4. F's proposal is sequentially rational; that is it maximizes F's expected utility, given F's updated beliefs and P's (and A's) optimal veto strategies.(7)

When there are multiple sequential equilibria for a given set of parameter values, the Pareto criterion will be used to select the most reasonable equilibrium; that is, an equilibrium is Pareto-optimal if no other equilibrium gives higher expected utility to either P or F without lowering the expected utility of the other. Therefore, when a nonpooling equilibrium exists, it must be shown that the players prefer that equilibrium to, say, a pooling equilibrium.

THE COMPLETE INFORMATION CASE

I shall now characterize the complete information equilibrium as a benchmark case. The complete information case also corresponds to Putnam's model, so I expect to find similar results.

When A does not have veto power and F has complete information, F will always offer x = t. Without A as a participant, F knows that P will accept any proposal in [0, t]. Thus, F will proposes t because it is the best outcome for F among the proposals in [0, t].

When A has veto power, F must offer a proposal that is acceptable both to A and P. In this case, F knows that in order to obtain P and A's approval, x must lie in [0, 2[x.sub.a]], as well as [0, t]. Given this, it is straightforward to show that F will offer x = min{t, 2[x.sub.a]}. Note that when t [less than] 2[x.sub.a], A's veto power does not reduce the size of the domestic win-set which remains at [0, t]. Thus Putnam's assumption that P can freely manipulate the size of the domestic win-set does not hold when A has preferences closer to F than P or A is more "dovish" than P. The equilibrium proposals in the complete information case are shown in Figure 3.

When [x.sub.a] [less than] t/2 (i.e., A is located farther from F than P), P ex post prefers the agent-veto regime because it prefers the agent-veto outcome 2[x.sub.a] to the unitary outcome t. When [x.sub.a] [greater than or equal to] t/2, however, P is indifferent between the agent-veto and unitary regimes because it gets t in either case; that is, when A is more opposed to F than P is, P can use A's veto power to extract more concessions from F. This is one illustration of Putnam's logic of two-level games.

Since P is never worse-off ex post with the agent veto, it is clear that P will also ex ante prefer the agent-veto regime to the unitary regime. Before showing this formally, let me make further simplification of the model by assuming that [t.sub.l] = 0 and that t is uniformly distributed over its domain. These assumptions will also simplify the presentation of equilibria in later analyses. Given these assumptions, P's expected utility under the unitary regime can be represented as

Q = - [integral of] [(t - t/2).sup.2] 1/[t.sub.h] dt between limits [t.sub.h] and 0,

since the bargaining outcome is always t. In contrast, P's expected utility G under the agent-veto regime is

G = - [integral of] [(t - t/2).sup.2] 1/[t.sub.h] dt between limits 2[x.sub.a] and 0 - [integral of] [(2[x.sub.a] - t/2).sup.2] 1/[t.sub.h] dt between limits [t.sub.h] and 2[x.sub.a],

since the bargaining outcome is t in the interval [0, 2[x.sub.a]] and 2[x.sub.a] in the interval [2[x.sub.a], [t.sub.h]]. It is straightforward to show that G [greater than or equal to] Q for all values of [x.sub.a] as shown in Figure 4.

P prefers to give veto power to A, regardless of A's preferences, because P always gets t under the unitary regime, which is no better than q. Under the agent-veto regime, the bargaining outcome is 2[x.sub.a] which is strictly better than q for some types of P. The other types of P reject 2[x.sub.a] in favor of q, but they are not worse off, because they get only t under the unitary regime.(8)

The result that P will always prefer the agent-veto regime under complete information may be interesting but is not empirically compelling.(9) It is not true that principals always give veto power to their agent, regardless of the latter's preferences. For instance, Congress has been trying to take away the veto power of the president in Section 301 trade negotiations.(10) Moreover, the president does not always submit an international agreement for ratification (Pahre 1994). In parliamentary systems, the prime minister does not have to submit an agreement for ratification at all (Milner 1993). Since the predictions of the complete information case do not seem to be supported empirically, I now turn to the incomplete information case in which P's preferences are private information.

THE INCOMPLETE INFORMATION CASE

Under the assumption of complete information, P always favors the agent veto because it gets only t if it does not use the agent veto. When F has incomplete information on t, however, it can no longer offer t and have it accepted by P under the unitary regime. Thus the unitary regime under incomplete information must be better for P than under complete information. In the following analysis, I will show that when F does not have complete information on t, P can become actually better off under the unitary regime than under the agent-veto regime.

The Unitary Regime

When F has incomplete information about t and P does not grant veto power to A, only a pooling equilibrium exists. That is, P is unable to transmit any information to F, where "information" means that F revises its beliefs about P's types based on P's message.

To see this, suppose that there are two types of P, m and n, such that n [greater than] m. Note that type n (m) is indifferent between the status quo and proposal n (m), which is what F offers when it thinks p is type n (m). I also assume that type n's preferences are such that it prefers proposal m to proposal n. Since there are only two types of P, information is transmitted only if P reveals its true type in equilibrium. If it does, F will propose n when P's type is n and m when P's type is m, because F knows in equilibrium that P is revealing its true type. However, given this proposal strategy by F, truth telling cannot be P's equilibrium strategy because type n, which prefers proposal m to proposal n, will mimic type m (i.e., sends a message saying that it is of type m, not type n). Thus the truth-telling equilibrium does not exist, so no information can be transmitted under the unitary regime.

From F's perspective, type n in this example is more moderate than type m. Unfortunately for F, the moderate type n does not want to reveal its type because if it does, F will offer it a proposal that is no better than q. As a result, the moderate type tries to bluff the foreign country to gain more concessions (i.e., mimics the hard-liner [type m]), and P does not transmit any information to F. This result based on the two-type case can be generalized to the continuous type case. The following proposition, the proof of which is provided in the Appendix, formally states this result:

PROPOSITION 1 (THE UNITARY EQUILIBRIUM). When A does not have veto power, no information is transmitted (i.e., only a pooling equilibrium exists) so that F must make a proposal based on its prior beliefs.

The equilibrium proposal [x.sub.1] by F (see the Appendix) can be derived as

[Mathematical Expression Omitted].

In this equilibrium, P rejects F's proposal with positive probability. Since the type t [element of] [0, [x.sub.1]) rejects proposal [x.sub.1], the probability of ratification is

[t.sub.h] - [x.sub.1]/[t.sub.h].

Figure 5 graphically illustrates the unitary equilibrium.

P's expected utility N in the unitary equilibrium is

N [equivalent to] - [integral of] [(q - t/2).sup.2] 1/[t.sub.h] dt between limits [x.sub.1] and 0 - [integral of] [([x.sub.1] - t/2).sup.2] 1/[t.sub.h] dt between limits [t.sub.h] and [x.sub.1].

When t [less than or equal to] [x.sub.1], P rejects F's equilibrium proposal [x.sub.1], so q is the bargaining outcome. When t [greater than or equal to] [x.sub.1], however, the bargaining outcome is [x.sub.1]. Note that N is constant in [x.sub.a]. Since A does not participate in the negotiation, P's ex ante utility is independent of A's preferences.

The Agent-Veto Regime

When A has veto power, P can credibly send information to F. To see this, note that when A has veto power, F never makes a proposal greater than 2[x.sub.a], regardless of its beliefs about t, because such a proposal will be rejected by A with certainty. Therefore, F's proposal must lie in [0, 2[x.sub.a]].(11) In particular, F will propose 2[x.sub.a] if it believes that t [element of] [2[x.sub.a], [t.sub.h]]. When t is greater than 2[x.sub.a], P knows that if it tells the truth and F believes it, F will propose x = 2[x.sub.a], which is the best proposal that F can make to obtain A's support. Thus, if 2[x.sub.a] is sufficiently attractive to P relative to what P obtains by bluffing, P has an incentive to tell the truth when t [element of] [2[x.sub.a], [t.sub.h]]. That is, if P's preferences diverge too much from those of A, P will reveal its type and accept 2[x.sub.a], because it fears that F may offer a proposal even worse than 2[x.sub.a]. The following proposition formally states this result:

PROPOSITION 2 (THE INFORMATIVE EQUILIBRIUM).

When A's ideal point is relatively small (i.e., [Mathematical Expression Omitted]), the following constitutes an equilibrium:(12)

1. P rejects F's proposal if it makes it strictly worse-off than the status quo outcome; P accepts it, otherwise. A has a similar veto strategy.

2. P sends a truthful message that its type is either in [0, [t.sub.1]] or [[t.sub.1], [t.sub.h]], where

[Mathematical Expression Omitted].

3. F's updated beliefs are consistent with P's equilibrium signaling strategy.

4. If the message indicates t [element of] [0, [t.sub.1]], F proposes

[Mathematical Expression Omitted].

If the message indicates t [element of] [[t.sub.1], [t.sub.h]], F proposes 2[x.sub.a].

If [x.sub.a] is sufficiently large, i.e., [Mathematical Expression Omitted], only a pooling equilibrium exists in which F makes a proposal based on its prior beliefs, that is, [[Pi].sup.*] = [x.sub.1] in equation 1.

The informative equilibrium is also illustrated in Figure 5. It is straightforward to see that P has no incentive to deviate from the equilibrium signaling strategy. When t [element of] [0, [t.sub.1]], P has a choice to tell the truth or lie. If P tells the truth, it expects F to propose [x.sub.2]. If it lies, it expects F to propose 2[x.sub.a]. Those types in [0, [t.sub.1]] prefer [x.sub.2] to 2[x.sub.a], because t [less than or equal to] [t.sub.1] = 2[x.sub.a] + [x.sub.2]. Thus P has no incentive to lie when t [element of] [0, [t.sub.1]]. Using a similar argument, I can show that P has no incentive to lie when t [element of] [[t.sub.1], [t.sub.h]].

The probability [[Rho].sub.d] of ratification in the informative equilibrium is

[[Rho].sub.d] = [t.sub.h] - [x.sub.2]/[t.sub.h],

because only types in [0, [x.sub.2]] will reject F's equilibrium proposal. Since [x.sub.2] is increasing in [x.sub.a], we see that the probability of ratification actually increases as A's ideal outcome becomes smaller and more opposed to F. This result seems to be inconsistent with another conjecture by Putnam that greater domestic constraints decrease the probability of ratification. According to Putnam, P's domestic constraints become greater when [x.sub.a] decreases, because the set of proposals that A prefers to the status quo - A's win-set - becomes smaller.

According to Putnam, a country's small win-set makes its bargaining position too inflexible and extreme against the foreign country, leaving little room for agreement. Putnam, however, does not consider how the foreign country will rationally respond to a smaller win-set. In my model, even with a smaller win-set, the foreign country will make a proposal that A will accept because it likes the status quo even less. At the same time, the probability of ratification increases because a smaller [x.sub.a] forces F to make a proposal that is acceptable to more types of P. Thus we find that the relationship between the size of a country's win-set and the probability of ratification cannot be established without knowing players' equilibrium response to changes in the size of the win-set.

To evaluate P's incentive to use the agent veto, I calculate P's expected utility H in the informative equilibrium:

H [equivalent to] - [integral of] [(q - t/2).sup.2] 1/[t.sub.h] dt between limits [x.sub.2] and 0 - [integral of] [([x.sub.2] - t/2).sup.2] 1/[t.sub.h] dt between limits [t.sub.1] and [x.sub.2] - [integral of] [(2[x.sub.a] - t/2).sup.2] 1/[t.sub.h] dt between limits [t.sub.h] and [t.sub.1],

where the bargaining outcome is q in the interval [0, [x.sub.2]], [x.sub.2] in the interval [[x.sub.2], [t.sub.1]] and 2[x.sub.a] in the interval [[t.sub.1], [t.sub.h]]. Differentiating with respect to [x.sub.a] yields

[Delta]H/[Delta][x.sub.a] = -2 [integral of]([x.sub.2] - t/2) [Delta][x.sub.2]/[Delta][x.sub.a] 1/[t.sub.h] dt between limits [t.sub.1] and [x.sub.2] - 4 [integral of] (2[x.sub.a] - t/2) 1/[t.sub.h] dt between limits [t.sub.h] and [t.sub.1].

The sign of this derivative is indeterminate because the signs of the integrands, ([x.sub.2] - t/2) and (2[x.sub.a] - t/2), depend on the values of t. A change in [x.sub.a] has a positive effect on types of P in [2[x.sub.2], [t.sub.1]] and [4[x.sub.a], [t.sub.h]] but a negative one on those in [[x.sub.2], 2[x.sub.2]] and [[t.sub.1], 4[x.sub.a]]. Numerical analysis shows that as [x.sub.a] increases, H first increases and then decreases. As [x.sub.a] increases, the bargaining outcomes in the informative equilibrium become more attractive to more types of P, thus increasing P's expected utility. However, as [x.sub.a] approaches [t.sub.h]/2, those outcomes become too large for most types of P and as a result, P's expected utility decreases.

Figure 6 draws P's expected utility under the agent-veto regime as a function of [x.sub.a]. It is represented by H for [Mathematical Expression Omitted], and N for [Mathematical Expression Omitted]. When [Mathematical Expression Omitted], P's expected utility equals N because only a pooling equilibrium exist in that case.

The Choice of Domestic Bargaining Regime

The choice of domestic bargaining regime affects the international bargaining equilibrium. Thus, if we compare P's expected utilities in the agent-veto and unitary equilibria, we can gain insight into P's incentive to choose one regime over the other.

Figure 6 shows that when [x.sub.a] is between [Mathematical Expression Omitted] (at which H intersects N) and [Mathematical Expression Omitted], P's expected utility is strictly higher under the agent-veto regime than under the unitary regime. Therefore, P will grant veto power to A only if [Mathematical Expression Omitted].

Let us interpret this result in terms of P and A's preferences. First, A's ideal point must lie within the domain [0, [t.sub.h]/2] of the distribution of P's ideal points. Moreover, since [Mathematical Expression Omitted], as Figure 6 shows,(13) we can say that P will grant veto power to A if A's ideal point is closer to P's expected ideal point E([x.sub.p]) which is [t.sub.h]/4. The average distance between [x.sub.a] and [x.sub.p], is the minimum at [x.sub.a] = [t.sub.h]/4 and continuously increasing in [x.sub.a] on both sides of the minimum. Thus veto power will be granted to A if, on average, A's ideal point is close to P's.

PROPOSITION 3. The principal will give veto power to its agent only if their preferences are similar, that is, the distance between their ideal points is small.

A numerical example can provide more insight into the kinds of A to whom P wants to grant veto power. Suppose that P's ideal point [x.sub.p] is uniformly distributed over the interval [0, .4] with mean E([x.sub.p]), of .2. Numerical analysis shows that in this case, [Mathematical Expression Omitted] and [Mathematical Expression Omitted]. Thus, P will grant veto power if A's ideal outcome [x.sub.a] lies in the interval (.093, .224). Since [Mathematical Expression Omitted], A's ideal outcome must be relatively close to P's expected ideal outcome. The results also show that among the acceptable agents, relatively more of them have hard-line positions against F in the sense that their ideal outcome is farther from F's ideal outcome than from P's expected ideal outcome; that is, [Mathematical Expression Omitted].

In the example above, A's veto power makes P strictly worse-off only if [x.sub.a] is very small relative to E([x.sub.p]), that is, [Mathematical Expression Omitted]. P is indifferent between the two regimes when [Mathematical Expression Omitted]. Thus, unless A's ideal outcome is very close to the status quo, P does not prefer the unitary regime to the agent-veto regime.

The attractiveness of the agent veto to P reflects two factors: (1) the veto's effect on the range of proposals that F can make - called the range reduction effect - and (2) its effect on the amount of information transmitted to F.

To isolate the range reduction effect, consider a pooling equilibrium under the agent-veto regime. Although I characterize only the informative equilibrium when [Mathematical Expression Omitted] in proposition 2, a pooling equilibrium also exists. P's expected utility in that pooling equilibrium is G when 2[x.sub.a] [less than] [x.sub.1] and N when 2[x.sub.a] [greater than or equal to] [x.sub.1] (see the proof of proposition 2 in the Appendix). As Figure 6 shows, even if no information is transmitted, the range reduction effect of A's veto power can be ex ante beneficial to P, because G [greater than] N when [Mathematical Expression Omitted]. Since E([x.sub.p]) = [t.sub.h]/4 [greater than] [x.sub.1]/2, this means that to receive veto power, A must have an ideal outcome that is, on average, farther from F's ideal outcome than P's ideal outcome is but not too far. A's ideal outcome must also be relatively close to P's expected ideal outcome. When A's ideal outcome is in that range, its veto power induces a foreign proposal that is better for most types of P. This range reduction effect is an incomplete information version of the benefit of a domestic constraint in two-level games.

Unlike the complete information version, however, the alignment of preferences between P and A matters when F has incomplete information about P's preferences. In the incomplete information case, A's veto power provides additional benefits to P, because it allows information to be transmitted between P and F. This informational effect is captured by the difference between F and G. Since H [greater than or equal to] G, P is willing to give veto power to more types of A than what the range reduction effect alone allows.

CONCLUSION

Putnam's conjecture that negotiators can benefit from their domestic constraints has implications for the design of domestic bargaining regimes in two-level games. If domestic constraints are as beneficial as Putnam suggests, negotiators have an incentive to impose domestic constraints on themselves before negotiating with their foreign counterparts. To examine this issue more closely, I develop a model of two-level games in which a negotiator decides whether to impose a domestic constraint on itself by granting veto power to an agent before negotiating with a foreign country.

I show that the negotiator's decision to create a domestic constraint depends in large part on whether or not the foreign country has information about the negotiator's preferences. If the foreign country has complete information, the negotiator will always grant veto power to the agent. Given the foreign country's knowledge of its preferences, the negotiator does not have much leverage without the agent veto.

When the foreign country has incomplete information about the negotiator's preferences, the negotiator will not always grant veto power. If the agent's preferences diverge too much from the negotiator's, the negotiator will choose the unitary regime where the agent has no veto authority. However, I also show that the range of agent preferences acceptable to the negotiator is surprisingly large. That is, the negotiator retains strong preference for the agent veto even when the foreign country has incomplete information.

The attractiveness of the agent veto to the negotiator comes from its range reduction and informational effects. The agent's veto power reduces the range of proposals that the foreign country can successfully make. If the agent's ideal point is not too far from a negotiator's ideal point, the negotiator benefits from this range reduction effect because it may induce the foreign country to make a proposal more favorable to the negotiator. The informational effect of the agent veto refers to better information transmission between the negotiator and the foreign country. By granting veto power to the agent, the negotiator can transmit more information in equilibrium to the foreign country and capture informational gains that would be lost in the absence of the agent veto. These informational gains give the negotiator an additional incentive to grant veto power to the agent.

The strategic granting of veto power to an agent is not limited to the case of international negotiations. The House-Senate bargaining in Congress also has this institutional feature. Before final passage, the House and the Senate form a conference committee to reconcile differences in bills. Representing the interests of the House floor, the Speaker of the House chooses House conferees. Thus the House floor is a principal and House conferees are its agents. Explaining the choice of conferees is an important issue in the congressional literature (Krehbiel 1991). Some have argued that conferees enjoy certain procedural advantages in bargaining with the Senate, such as veto power (Shepsle and Weingast 1987). If so, then the question of who goes to conference may be construed as asking to whom the House floor chooses to give veto power.

The model presented here predicts that given restrictive conference procedures, the House floor will choose non-preference outliers, that is, members with preferences similar to the House floor. This is consistent with Krehbiel's (1991) empirical finding that controlling for other influences, conferees tend to be non-preference outliers.(14) Moreover, the model explains why and how legislators' preferences affect the choice of conferees by the House floor. In bargaining with the Senate, the House may reap informational gains by using conferees as a means to reduce the Senate's uncertainty about House preferences. This device, however, is not beneficial for the House floor if the conferees have preferences too divergent from those of the floor.

APPENDIX

The Definition of a Sequential Equilibrium

In the definition given below, A has veto power. An equilibrium for the case in which A has no veto power can be defined without E2 and without [Mathematical Expression Omitted] in the conditional probability in E5.

A sequential equilibrium consists of strategies ([m.sup.*], [Mathematical Expression Omitted], [Mathematical Expression Omitted], [[Pi].sup.*]) and F's beliefs [[Mu].sup.*] about t satisfying E1-E5:

E1. For all [Mathematical Expression Omitted].

E2. For all x [element of] X and t [element of] T, [Mathematical Expression Omitted].

E3. For all t [element of] T, [Mathematical Expression Omitted].

E4. If [m.sup.*] - 1(s) [not equal to] 0, then [[Mu].sup.*]([center dot], s) satisfies Bayes' Rule according to [[Pi].sup.*]([center dot]) and prior belief f([center dot]).

E5. For all s [element of] S, [u.sub.f]([[Pi].sup.*](s)) [greater than or equal to] [u.sub.f](q), and

[[Pi].sup.*](s) [element of] [argmax.sub.x[element of]X][Beta](x[where]s)[u.sub.f](x) + (1 - [Beta](x[where]s))[u.sub.f](q),

where [Beta](x[where]s) is the conditional probability that x is accepted,

[Mathematical Expression Omitted].

PROPOSITION 1. Under the unitary regime, there can be only one elicited proposal in a sequential equilibrium.

Proof. Suppose to the contrary that two proposals, say [a.sub.1] and [a.sub.2], are elicited in some equilibrium.

Let [a.sub.2] [greater than] [a.sub.1] and P's preference ordering be denoted by [Mathematical Expression Omitted], so [Mathematical Expression Omitted] if P prefers [a.sub.1] to [a.sub.2]. Then, [Mathematical Expression Omitted] if [x.sub.p] [greater than] [a.sub.1] + [a.sub.2]/2 or t [greater than] [a.sub.1] + [a.sub.2]. Since [a.sub.1] + [a.sub.2], t [greater than or equal to] [a.sub.2] is willing to accept both [a.sub.2] and [a.sub.1], but prefers not to elicit [a.sub.2] because [Mathematical Expression Omitted]. Thus, when F is supposed to propose [a.sub.2], it believes that t is not in [[a.sub.2], [a.sub.1] + [a.sub.2]). Given its beliefs that t [less than] [a.sub.2] or t [greater than or equal to] [a.sub.1] + [a.sub.2], proposing [a.sub.2] cannot be optimal for F because proposing [a.sub.2] + [Epsilon] has the same probability of being accepted by P as [a.sub.2] but gives higher utility to F. This contradicts the definition of a sequential equilibrium.

F's Problem in a Pooling Region.

When F believes that t is in some subset, say [[Alpha], [Beta]], of T, its proposal problem is more complicated than the complete information case. In this section, I derive F's optimal proposals x in that pooling region. If x [greater than] [Beta], the proposal is rejected with probability 1 and x [less than] [Alpha], the proposal is accepted with probability 1. If [Alpha] [less than or equal to] x [less than or equal to] [Beta], the probability of the proposal being accepted is ([Beta] - x)([Beta] - [Alpha]). Thus F's expected utility when it makes a proposal (x, 1) in the pooling region [[Alpha], [Beta]], is [Mathematical Expression Omitted].

To find the optimal x when x [element of] [[Alpha], [Beta]], I rewrite K(x) as

K(x) = [x.sup.3] - (2 + [Beta])[x.sup.2] + (2[Beta])x - [Beta] + [Alpha]/[Beta] - [Alpha].

The optimal x maximizes K(x) in [[Alpha], [Beta]] and depends on the shape of K(x) in that interval. Since K(0) = -1, K([Alpha]) = -[([Alpha] - 1).sup.2], and K([Beta]) = -1, it is straightforward to show that K(0) = K([Beta]) [less than] K([Alpha]). To determine whether K(x) can be larger than K([Alpha]) in ([Alpha], [Beta]), differentiate K(x) with respect to x, which yields

[Delta]K/[Delta]x = 3[x.sup.2] - 2(2 + [Beta])x + 2[Beta]/[Beta] - [Alpha].

It follows that

[Delta]K/[Delta]x(0) = 2[Beta]/[Beta] - [Alpha] [greater than] 0, [Delta]K/[Delta]x([Beta]) = [[Beta].sup.2] - 2[Beta]/[Beta] - [Alpha] [less than] 0,

[Delta]K/[Delta]x(1) = -1/[Beta] - [Alpha] [less than] 0,

and

[Delta]K/[Delta]x(2) = 4 - 2[Beta]/[Beta] - [Alpha] [greater than] 0.

Thus K(x) has a local maximum between [Beta] and 0 at

x = [x.sup.*] = 2 + [Beta] - [square root of [[Beta].sup.2] - 2[Beta] + 4]/3.

If [x.sup.*] [greater than or equal to] [Alpha], the optimal x in [[Alpha], [Beta]] is [x.sup.*], and if [x.sup.*] [less than] [Alpha], the optimal x is [Alpha]. The sign of [Alpha] - [x.sup.*] is the opposite sign of

[Delta]K/[Delta]x([Alpha]) = 3[[Alpha].sup.2] - 4[Alpha] - 2[Beta][Alpha] + 2[Beta]/[Beta] - [Alpha].

PROPOSITION 2.

[Mathematical Expression Omitted],

the unique Pareto-optimal equilibrium is characterized by

[Mathematical Expression Omitted],

[Mathematical Expression Omitted],

and

[Mathematical Expression Omitted],

where

[Mathematical Expression Omitted]

and

[Mathematical Expression Omitted].

b. If [Mathematical Expression Omitted], only a pooling equilibrium exists in which [[Pi].sup.*] = [x.sub.1] in equation 1.

Proof of a. First, I show that P does not have an incentive to deviate from the equilibrium signaling strategy. If t [element of] [0, [t.sub.1]] deviates and sends [s.sub.2], P expects F to propose 2[x.sub.a]. Types in [0, [x.sub.2]] are indifferent between [x.sub.2] and 2[x.sub.a] because they will reject both. But types in [[x.sub.2], [t.sub.1]] prefer [x.sub.2] to 2[x.sub.a] because [t.sub.1] = 2[x.sub.a] + [x.sub.2] represents the type that is indifferent between [x.sub.2] and 2[x.sub.a]. Thus no type in [0, [t.sub.1]] strictly prefers to deviate. Likewise, types in [[t.sub.1], [t.sub.h]] do not have an incentive to deviate and send [s.sub.1] because they prefer 2[x.sub.a]to [x.sub.2]. Given P's equilibrium signaling strategy, F's beliefs are rational.

It remains to show that F's equilibrium proposals are optimal, given its equilibrium beliefs. When F receives s [not equal to] [s.sub.1], it believes that t [element of] [[t.sub.1], [t.sub.h]] and proposes 2[x.sub.a], which is the best outcome for F given that belief. When F receives [s.sub.1], it believes t [element of] [0, [t.sub.1]]. Because of A's veto power, F will not propose any x greater than 2[x.sub.a]. If F proposes some x [less than or equal to] 2[x.sub.a], its expected utility, given that belief, is

- ([t.sub.1] - x/[t.sub.1])[(x - 1).sup.2] - (1 - [t.sub.1] - x/[t.sub.1])[(q - 1).sup.2],

where (([t.sub.1] - x)/[t.sub.1]) is the probability of x being accepted. A unique interior solution to this maximization is [x.sub.2]. Since [x.sub.2] is always smaller than 2[x.sub.a], it is F's optimal equilibrium proposal.

Second, we need to show that the informative equilibrium is the unique Pareto-optimal equilibrium. This will be shown in two steps: (1) there is no sequential equilibrium in which more information is revealed than the informative equilibrium, and (2) the informative equilibrium Pareto-dominates a pooling equilibrium.

Using the same technique as in proposition 1, we can show that there can be only one elicited proposal in the interval [0, 2[x.sub.a]). This implies that there are at most two elicited proposals with 2[x.sub.a] being one of the two. The informative equilibrium has two elicited proposals, [x.sub.2] and 2[x.sub.a], so no other sequential equilibrium has more information revealed.

The only other sequential equilibrium is then a pooling equilibrium. F's equilibrium proposal in the pooling equilibrium is w [equivalent to] min{[x.sub.1], 2[x.sub.a]}. Thus P's expected utility in the pooling equilibrium is G when 2[x.sub.a] [less than] [x.sub.1] and N when 2[x.sub.a] [greater than or equal to] [x.sub.1]. To see this, when 2[x.sub.a] [less than] [x.sub.1], F knows that [x.sub.1] will be rejected by A and instead, offers 2[x.sub.a]. Then, if P's type is in [0, 2[x.sub.a]], P will reject 2[x.sub.a]; otherwise, P will accept it. Thus P's expected utility in this case will be G, the same as that in the complete information case with the agent veto. When 2[x.sub.a] [greater than or equal to] [x.sub.1], knowing that A will accept [x.sub.1], A will propose it as if there is no agent veto. Thus P's expected utility is N, the same as that in the unitary equilibrium.

Figure 6 shows that P's expected utility is not worse off in the informative equilibrium than in the pooling equilibrium, since H [greater than] G. Numerical analysis confirms that H [greater than] G in general.

F also prefers, ex ante, the informative equilibrium to the pooling equilibrium. To show this, let [C.sub.i] be F's expected utility in the informative equilibrium where

[C.sub.i] = - [integral of][(q - 1).sup.2] 1/[t.sub.h] dt between limits [x.sub.2] and 0 - [integral of] [([x.sub.2] - 1).sup.2] 1/[t.sub.h] dt between limits [t.sub.1] and [x.sub.2] - [integral of] [(2[x.sub.a] - 1).sup.2] 1/[t.sub.h] dt between limits [t.sub.h] and [t.sub.1].

[C.sub.p] is F's expected utility in the pooling equilibrium and can be expressed as a function of w:

[C.sub.p] = - [integral of] [(q - 1).sup.2] 1/[t.sub.h] dt between limits w and 0 - [integral of] [(w - 1).sup.2] 1/[t.sub.h] dt between limits [t.sub.h] and w.

Numerical analysis shows that [C.sub.i] [greater than or equal to] [C.sub.p]. Intuitively, F is better off in the informative equilibrium than in the pooling equilibrium because F's proposal is more likely to be accepted in the former, due to better information transmission. Therefore, the informative equilibrium Pareto-dominates the pooling equilibrium.

Proof of b. No information is transmitted in this equilibrium, so F in equilibrium makes a proposal based on its prior beliefs. When [Mathematical Expression Omitted], however, [x.sub.a] [greater than] [x.sub.1]/2 because [Mathematical Expression Omitted], so [[Pi].sup.*] = [x.sub.1], which is acceptable to A.

Notes

I would like to thank David Baron, David Epstein, Keith Krehbiel, and Harrison Wagner for helpful suggestions.

1. Putnam's idea that the domestic ratification process can be used as a bargaining advantage originates with Schelling (1960). According to Schelling, the use of a bargaining agent should be understood as a negotiator's attempt to commit to its preferred bargaining position. For example, "the use of a professional collecting agency by a business firm for the collection of debts is a means of achieving unilateral rather than bilateral communication with its debtors and of being therefore unavailable to hear pleas or threats from the debtors" (pp. 142). The creditor using a collecting agency to commit to a uncompromising stance against the debtor corresponds to a negotiator granting veto power to another domestic actor in international negotiations.

2. Pahre (1994) is an exception, but he only looks at the complete information case and does not consider the case of incomplete information.

3. For other models of two-level games, see Iida 1993; Mayer 1992; Mo 1994.

4. Lax and Sebenius (1991) and Martin (1994) examine other sources of uncertainty in their bargaining models with internal conflict. Lax and Sebenius model an agent who is uncertain about the principal's preferences, while Martin's agent has private information that the principal does not have. These authors, however, do not address the signaling consequences of the agent's veto power.

5. Alternatively, P can choose a regime after P's type is revealed. In this case, the choice of a regime can signal P's type. For a similar problem in a legislative setting, see Gilligan and Krehbiel 1989.

6. Since S is continuous, an equilibrium in which a segment of T is truthfully signaled to the foreign country is not ruled out.

7. The formal statement of this equilibrium concept is given in the Appendix.

8. As an anonymous referee for this journal observes, if we relax the assumptions that both P and A prefer a negotiated outcome to the status quo or that F's ideal point is not acceptable to P and A in comparison to the status quo, P's incentive to give veto power to A weakens. For example, when [x.sub.a] [less than] q, A will always reject F's proposal that P may want to accept, so P will not give veto power to A in this case. If t and 2[x.sub.a] is greater than 1 (i.e., F's ideal point is acceptable to P and A), P does not need an agent to influence international bargaining outcome because F will always propose x = 1 which both A and P will accept.

9. This result corresponds to Pahre 1994, hypoth. 13.

10. As part of the 1988 omnibus trade bill, Congress sought to reduce the role of the president in Section 301 bargaining (Bello and Holmer 1990). Under the old law, the president had discretion in deciding whether to retaliate against unfair foreign trade practices. But Congress wanted to make retaliation automatic in some cases, revoking the president's veto power. For example, when a foreign practice in question violates U.S. rights under an existing trade agreement, the president must now retaliate against that foreign country. The fact that Congress initially permitted a presidential veto over Section 301 decisions but later decided to limit the veto shows that Congress does not always favor giving veto power to another domestic actor.

11. This assumes that 2[x.sub.a] [less than] [t.sub.h]. The case of 2[x.sub.a] [greater than or equal to] [t.sub.h], is uninteresting because A's veto power is irrelevant to F's proposal problem and the game is identical to the unitary regime case.

12. At [Mathematical Expression Omitted], [t.sub.1] = [t.sub.h]. See the Appendix for the closed form expression for [Mathematical Expression Omitted].

13. The first inequality is based on numerical analysis. The second inequality can be derived from the sign of

[Mathematical Expression Omitted],

which is positive.

14. Krehbiel also finds expertise effects; that is, conferees tend to be specialists. My model does not capture these expertise effects. In my model, all potential conferees can be thought of as having a common level of expertise, because their preferences are assumed to be well known. One can argue that as Congress members build their policy reputation in Congress, there is less uncertainty about their preferences.

References

Bello, Judith Hippler, and Alan F. Holmer. 1990. "The Heart of the 1988 Trade Act: A Legislative History of the Amendments to Section 301." In Aggressive Unilateralism, ed. Jagdish Bhagwati and Hugh T. Patrick. Ann Arbor: University of Michigan Press.

Evans, Peter B. 1993. "Building an Integrative Approach to International and Domestic Politics: Reflections and Projections." In Double-edged Diplomacy, ed. Peter B. Evans, Harold K. Jacobson, and Robert D. Putnam. Berkeley: University of California Press.

Gilligan, Thomas W., and Keith Krehbiel. 1989. "Collective Choice without Procedural Commitment." In Strategic Models of Politics, ed. Peter Ordeshook. Ann Arbor: University of Michigan Press.

Iida, Keisuke. 1993. "When and How Do Domestic Constraints Matter? Two-Level Games with Uncertainty." Journal of Conflict Resolution 37:403-26.

Krehbiel, Keith. 1991. Information and Legislative Organization. Ann Arbor: University of Michigan Press.

Lax, David A., and James K. Sebenius. 1991. "Negotiating through an Agent." Journal of Conflict Resolution 35:474-93.

Martin, Elizabeth. 1994. "An Informational Theory of Congressional Delegation." University of Iowa. Mimeo.

Matthews, Steven. 1989. "Veto Threats: Rhetoric in a Bargaining Game." Quarterly Journal of Economics 104:347-69.

Mayer, F. W. 1992. "Managing Domestic Differences in International Negotiations: The Strategic Use of Internal Side Payments." International Organization 46:793-818.

Milner, Helen. 1993. "The Interaction of Domestic and International Politics: The Anglo-American Oil Negotiation and the International Civil Aviation Negotiations, 1943-1947." In Double-edged Diplomacy, ed. Peter B. Evans, Harold K. Jacobson, and Robert D. Putnam. Berkeley: University of California Press.

Mo, Jongryn. 1994. "The Logic of Two-Level Games with Endogenous Domestic Coalitions." Journal of Conflict Resolution 38:402-22.

Pahre, Robert. 1994. "Who's on First, What's on Second: Actors and Institutions in Two-Level Games." University of Michigan. Mimeo.

Putnam, Robert D. 1988. "Diplomacy and Domestic Politics: The Logic of Two-Level Games." International Organization 42:427-60.

Schelling, Thomas C. 1960. The Strategy of Confiict. Cambridge: Harvard University Press.

Shepsle, Kenneth A., and Barry R. Weingast. 1987. "The Institutional Foundation of Committee Power." American Political Science Review 81:85-104.

Jongryn Mo is Assistant Professor of Government, University of Texas at Austin, Austin, TX 78712, and a National Fellow, The Hoover Institution, Stanford, CA 94305.
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