To Invite or Not to Invite a Lobby, That Is the Question

2.1 Assumptions

2.2 Double commitment and a bilateral transaction

If the lobby participates, a disclosure subgame involves the attention of both the policy-maker and the lobby. Thus, our game can be seen as a bilateral transaction, where both parties bring attention to the table and one party also brings money to the table. A normal version of the transaction is that the policy-maker trades his attention (willingness to listen), while the lobby offers both her attention (willingness to talk) and a payment. Nevertheless, our mechanism also permits transactions in which the policy-maker offers the payment. Thus, our paper is a generalization in a sense that it permits bilateral transactions of any kind, and this generalization deserves extra discussion.

Is our general mechanism with both positive transfers (access fees) and negative transfers (access compensations) realistic? In the following analysis, we derive the necessary conditions for the implementation of both types of transfers. Formally, we analyze which restrictions upon the player’s actions in our game are necessary if we compare our game with a game in which the timing is identical but no restrictions on the action space exist in Stage 3. In the non-restricted game, Stage 3 can be modeled as a simultaneous game in which the lobby’s message space is {∅,0,1} and the policy-maker’s attention space is {listen,notlisten}.

The first necessary restriction for the implementation of our game is the existence of the policy-maker’s conditional commitment to not listen. (Conditionality means that an action is conditional upon the transfer realization.) In the absence of this commitment, the policy-maker’s weakly dominant action in Stage 3 is to listen. This limits the policy-maker’s opportunity to extract access fees. The second necessary restriction is the lobby’s conditional commitment to not talk. In the absence of this commitment, if the policy-maker is expected to listen, then under skeptical beliefs, m=∅ is interpreted as a low type, and hence, the lobby reveals her information. This limits the lobby’s opportunity to extract access compensations, and the game boils down to an access fee game in which only the scenario with access fees is feasible.

Our mechanism is therefore implemented only if the policy-maker can conditionally commit to not listen and the lobby can conditionally commit to not communicate. For each player, the condition of the commitment is that a realized transfer is consistent with the player’s proposal. The existence of the double conditional commitment gives each trading party a disagreement point that is independent of the action of the other party and of the level of the proposed fee. Thus, we can indeed interpret the game as a bilateral transaction.

The two commitments are not active at the same time, however. If the proposed transfer is positive and the policy-maker is the beneficiary, only the policy-maker’s commitment is active. If the proposed transfer is negative and the lobby is the beneficiary, only the lobby’s commitment is active.

How should one interpret the double commitment in the context of lobbying? The policy-maker’s commitment device is often attributed to the existence of tight schedules. In the absence of free time slots, the policy-maker cannot devote the minimal required attention to the extra policy agenda and must rely on his (prior or skeptical) belief. The lobby’s commitment device might originate in circumstances when an extra action is necessary before communication. For example, in many agendas, hiring a connected agent in advance is a precondition of successful lobbying (Bertrand, Bombardini, and Trebbi 2014). Alternatively, the lobby’s private signal may not be verifiable, and the lobby needs to generate the verifiable signal in advance to be able to communicate the message.

Finally, the transfers must be carefully interpreted. While fees are normally interpreted to be campaign contributions, compensations may be in the form of base earmarks or subsidies that the policy-maker can credibly provide. The credibility of the negative transfer may rise in particular when the policy-maker provides informational benefits (e.g. departmental reports, regulatory prospects, or any other valuable data about a topic separate from the analysis). In such a case, the policy-maker offers a meeting to discuss this information with the lobby, and during such a meeting, the lobby cannot avoid being subject to the questions that imply the disclosure of her type.

3.1 Two skeptic refinements

We will show that both timings can be solved in an identical way. For this purpose, we apply two standard refinements. (The equilibria that do not comply with these standard refinements are analyzed in the extensions.) Both refinements intuitively mean that the policy-maker has skeptical beliefs. As a skeptic, the policy-maker interprets non-participation or non-disclosure to be a signal of the low type of the lobby, as long as such an equilibrium exists.

First, in the disclosure stage, we restrict ourselves to profiles for which both types of lobbies are willing to disclose their evidence. To determine these profiles safely, we set the out-of-equilibrium belief for non-disclosure d=0 as the minimal posterior π0. Intuitively, non-disclosure is interpreted to characterize a low type of the lobby. Under these beliefs, the low type of the lobby is indifferent between disclosure and non-disclosure because both induce an identical posterior from the policy-maker. This assumption complies with the intuitive criterion of Cho and Kreps (1987).

The next refinement applies to interim access only, where signaling subgames that begin with a private observation may involve two pure-strategy equilibria. In an equilibrium, either both types of lobbies are pooled, (e0,e1)=(0,0), or both types are separated, (e0,e1)=(0,1). In the spirit of the unraveling argument by Milgrom (1981), we focus on the separating equilibrium only, if separation exists.

3.2 Bargaining perspective

A helpful perspective upon the game is a transaction (bargaining) perspective where both the policy-maker and the lobby must agree to the transfer so that the evidence is disclosed. The application of the transaction perspective depends on timing, because timing determines the identity of the bargaining partner of the policy-maker. For ex ante access, the lobby is the bargaining partner. For interim access, only the high type of the lobby is the bargaining partner. ^[4] Given the change in the identity, timing affects the outside option of the partner, the partial gains of the partner, the partial gains of the policy-maker, and the bargaining surplus.

The bargaining protocol is a single take-it-or-leave-it offer: In Stage 1, the policy-maker makes an offer. In Stage 2, the partner agrees or disagrees. The equilibrium under this protocol is easily found as follows:

1. Calculate the positive or negative partial gains of the agreement (a.k.a. values of access) for each bargaining party. The sum of the partial gains defines the bargaining surplus.

2. If the surplus is non-negative, the policy-maker offers a transfer that exactly meets the partner’s participation condition. We say that the policy-maker invites his partner. Therefore, the policy-maker extracts all partial gains of the partner and seizes full surplus. The partner is left with her outside option.

3. If the surplus is negative, the policy-maker offers a prohibitively high transfer. We say that the policy-maker does not invite his partner. The partner disagrees.

3.3 Bargaining surplus

Consider first the policy-maker. His outside option is independent of the timing of the signal realization. Namely, his outside option is described by her prior beliefs and the action corresponding to her prior beliefs, to be denoted aθ. Clearly, we have aθ=1πθ>12. At the outside option, his expected loss is Eθ(πθ):=E(aθ;πθ)=min{πθ,1−πθ}V.

If the partner agrees, the policy-maker learns new information, updates his beliefs, and may change his action. For an uninformative signal, there is no effect on the policy-maker’s action. Therefore, the policy-maker’s partial gain is zero. For an informative signal, the expected loss drops from Eθ(πθ) to Ee(α,β,πθ):=[απθ+β(1−πθ)]V.

To obtain the remaining bargaining variables, we have to distinguish between the timings of the signal realization.

3.4 Lack of communication

We use the surpluses to identify the necessary conditions for a negative value of the surplus. Under our treatment of indifferences that favor participation, a negative surplus is equivalent to setting a prohibitive transfer.

Proof. Using the bargaining perspective, a sufficient and necessary condition for a prohibitive transfer is negative surplus. To identify the negative surplus, we prove inequalities in eqs [2] and [3]. It is sufficient to recall that f(α,β,πθ)≥0 and Eθ(πθ)≥Ee(α,β,πθ). The surplus can be negative only in the first case of eq. [2], where access is ex ante, the status quo is favorable for the lobby, and the signal is informative.□

3.5 Noise and prohibitive transfer

When the bargaining surplus is negative, the policy-maker cannot compensate the lobby for her participation without making himself worse off. The source of the negative surplus lies in the attractiveness of the lobby’s outside option, which makes the agreement to disclose the evidence prohibitively costly.

In this section, we focus in detail on the existence of the prohibitive transfer in the parametrical space (α,β,πθ,V). By Proposition 1, it is sufficient to consider only the timing under ex ante access and the case of πθ>12, which implies favorable status-quo action aθ=1.

In the first step, we find that for any V>0, a set of informative signals exists such that the access is strategically restricted. Such signals are found in the neighborhood of the informative signal with the maximal α-error and minimal β-error, (α,β)=1−πθπθ,0. This result occurs because the corresponding surplus with this signal is negative,

To understand the role of noise in more detail, we examine the iso-surplus curves. The iso-surplus curves are linear in the signal space (α,β), because the partial derivatives are independent of (α,β),

The key curve is the zero-surplus curve, S(α,β,πθ)=0. By simple algebra, the curve is defined by

The zero-surplus curve always originates from the NW corner, because S(0,1,πθ)=0. The shape of the curve depends on V⋛1:

1. The policy-maker’s valuation exceeds the lobby’s valuation (V>1): From eqs [6] and [7], the iso-surplus curves move from NW to SE. Informative signals with low noise have a positive surplus, and informative signals with large noise have a negative surplus.

2. Both valuations are identical (V=1): The iso-surplus curves move from N to S. Hence, informative signals with α=0 have exactly a zero surplus. Any other informative signal features a negative surplus.

3. The lobby’s valuation exceeds the policy-maker’s valuation (V<1): The iso-surplus curves move from NE to SW. All informative signals have a negative surplus.

Figure 1

The shape of the zero-surplus curve for πθ≥12

Figure 1 illustrates. In the signal space, we thus recognize three types of signals:

1. Small noise: The signal is informative, and the surplus is non-negative. In the equilibrium, the lobby participates. For V<1, the set is empty.

2. Moderate noise: The signal is informative, but the surplus is negative. In the equilibrium, participation is prohibitively costly for the lobby. The set is non-empty.

3. Large noise: The signal is uninformative, and the surplus is zero. In the equilibrium, the status quo is maintained. The set is non-empty.

The surplus is non-monotonic at a structural switch from an informative to an uninformative signal. Namely, at β=1−απθ1−πθ, the negative surplus changes into a zero surplus. This non-monotonicity associated with a structural switch is strategically relevant in the setting in which signals are endogenous to the players (see Section 5).

3.6 Alternative regimes

Our model considers commitments that are conditional on the realization of the transfer; the policy-maker is committed to not listen, and the lobby is committed to not communicate if the transfer is not realized. What if a certain commitment is missing? This case is analyzed in Table 1. The table also considers plain commitments that are not conditional on the transfer. Table 1 solves the equilibria for alternative regimes, depending on the structure of commitments (none, unilateral, bilateral) and the type of commitments (plain, conditional).

We have three configurations of preferences that depend on the sign of the lobby’s gains and the sign of the surplus. If both commitments are present, then in each configuration, exactly one of the two commitments is active and one is passive. Making the passive commitment absent has no effect on the equilibrium; only the absence of the active commitment matters.

Interestingly, the type of the commitment fully characterizes the effect of its absence. By making the commitment to not listen passive, the effect is redistributive but not informative. In contrast, by making the commitment to not talk passive, the effect is informative but not redistributive. A consequence of this property is that a loss of the commitment to not listen has no effect on the equilibrium if the commitments are plain; such a loss may have only a redistributive effect, but redistribution is by definition absent for plain commitments.

Additionally, because the sum of the player’s utilities is measured by the amount of information, only the existence of the commitment to not talk may affect the sum. (This observation is used in the utilitarian welfare analysis in the following Section 4.) From that perspective, only the lobby’s commitment is essential for understanding the strategic non-participation.

Notice that the regimes with a unilateral conditional commitment can be achieved by augmenting our game through restricting the action space of the proposed transfers. The regime with a unilateral commitment to not listen is equivalent to the assumption that the proposed transfer is non-negative, cP≥0 (only access fees), and the regime with a unilateral commitment to not talk is equivalent to the assumption that the proposed transfer is non-positive, cP≤0 (only access compensations).

Finally, we can discuss the effects of the introduction of transfers; this can be interpreted such that plain commitments (Benchmark 2) turn into conditional commitments. As Table 1 reveals, the introduction of transfers implies that the positive surplus, which was previously not generated (because of the impossibility of compensating the lobby), is now seized by the policy-maker.

4.1 Non-benevolent policy-maker

We may represent the lobby’s objective as a loss function l:{0,1}→{0,1}, where l(a)=1−a. The utilitarian objective minimizes the sum of the policy-maker’s expected loss and the lobby’s expected loss. We first derive the first-best actions, (a0∗,a1∗). For a signal s and corresponding beliefs πs, the first-best action is

This expression can be reduced to

Notice that V−12V<12. Next, since posteriors are non-decreasing in the lobby’s type, π1∗≥π0∗, the optimal actions are also non-decreasing, a1∗≥a0∗. Recall that the equilibrium actions are also non-decreasing in the lobby’s type, a1≥a0.

We may expect two sources of welfare distortion:

1. In her ex post decision, the policy-maker neglects the negative externality of a low action on the lobby. Hence, the policy-maker is biased toward low action for any signal realization. Nevertheless, the bias does not need to be strong enough to make a difference between the equilibrium action as and the first-best action as∗.

2. In her ex ante decision, the policy-maker sacrifices information if he sets a prohibitive transfer. By Proposition 1, he takes such action only if access is ex ante and aθ=1. Consequently, a0=a1=1. Hence, we expect an extra status-quo bias toward the high action for any signal realization, if the transfer is prohibitive.

The two biases move in the opposite directions. Hence, it is interesting to understand which bias dominates if both biases are present at the same time. The next proposition derives the key observation; the status-quo bias exactly corrects for the negative externality. Somewhat surprisingly, the information loss is associated with a welfare-improving action, not vice versa.

Proof. Consider s=1. By Proposition 1, a necessary condition for a prohibitive transfer is aθ=1, which implies that πθ>12 and a0=a1=1. Then, π1≥πθ>12>V−12V, and consequently, a1∗=a1. There is no welfare distortion for the high signal realization, s=1.

Consider the low signal realization, s=0. If a0∗=1, then a0∗=a0, and there is no welfare distortion. If a0∗=0, then π0<V−12V, or equivalently,

However, eq. [11] is inconsistent with the negative surplus, which is a necessary condition for access restriction. By the zero-surplus equation in eq. [8], the negative surplus requires

□

The policy-maker’s prohibitive transfer increases the welfare because the two distortions cancel each other out. Put more precisely, the status-quo bias serves as a check for the externality bias; it guarantees the first-best action independently of the size of the externality bias. Thereby, the policy-maker ex ante improves the welfare relative to her ex post (non-contractible) actions.

Finally, we can briefly discuss the equilibrium properties when the lobby participates. By Proposition 2, we know that the only distortion occurs toward the low action. Hence, in terms of welfare, there are only three possibilities:

1. No distortion: If (a0,a1)=(1,1), then (a0∗,a1∗)=(1,1). This is one of the cases in which the equilibrium entails the first-best allocation. This equilibrium occurs if the status-quo action is the high action, and the signal is uninformative. ^[5]

2. Single distortion: For a single distortion, we must have the separating equilibrium, (a0,a1)=(0,1), and the first-best actions, (a0∗,a1∗)=(1,1). An example is the case of π1>12>πθ>π0>V−12V. These parameters guarantee that the lobby participates and that the signal is informative.

3. Double distortion: The existence of double distortion can be easily evaluated. Double distortion occurs if and only if (a0,a1)=(0,0) and (a0∗,a1∗)=(1,1). This equilibrium occurs only if the signal is uninformative and aθ=0 (or, equivalently πθ≤12). To obtain high actions that are socially optimal, we must have π0>V−12V. Because the signal is uninformative, we must also have π1≤12. To sum up, a necessary condition for double distortion is 12≥π1≥π0>V−12V.

4.2 Benevolent policy-maker with a mixed objective

Suppose the welfare measure is the sum of all players’ expected losses from the policy-maker’s actions. As in Grossman and Helpman (2001), the policy-maker’s objective is mixed. On one hand, the policy-maker is benevolent and accounts for the total expected losses (i.e. welfare). On the other hand, the policy-maker values her private benefits.

To obtain explicit microfoundations for the welfare, assume that we have three agents. Only Agent 1 is organized and can meet the policy-maker; hence, Agent 1 becomes a single lobby. (i) Agent 1’s loss function is l1(a)=1−a. (ii) Agent 2’s loss function is l2(a)=a. (iii) Agent 3’s loss function is l3(a,θ)=L(a,θ). The policy-maker has an action-independent loss function; alternatively, we may think of him as being either Agent 2 or Agent 3.

By definition, the total welfare loss is W(a,θ)=l1(a)+l2(a)+l3(a)−1=L(a,θ). Hence, ex post, the benevolent policy-maker with a mixed objective and posterior π sets the welfare-maximizing action a∈{0,1} exactly as in the previous analysis, namely to minimize E(a,π).

Ex ante, however, private gains matter. In the policy-maker’s mixed objective, the parameter of benevolence is λ. Hence, the policy-maker’s expected loss in signal realization s, is

When setting the access fees, the policy-maker’s objective is to minimize the ex ante loss, (1−f)U(a0,0)+fU(a1,1).

Finally, to keep our setting intact, the values of the fees must be identical for the lobby (Agent 1) and the policy-maker. The policy-maker treats her private gains exactly as the welfare loss of lobby only if λ=12. Obviously, this assumption does not imply that the policy-maker is a genuine altruist who treats the private benefits of the other agents as being equal to her private gains. In fact, the policy-maker discriminates between the sources of the losses of the other agents: (i) The loss of any agent is fully accounted for only if it is associated with the action that disfavors the agent. (ii) In contrast, the loss of an agent stemming from a private transfer to policy-maker is not considered at all. This dichotomy is important for the construction and interpretation of the welfare properties of the equilibrium.

Clearly, in this setting, the participation of the lobby is equivalent to having the maximal welfare. The welfare distortion arises only if the information available to the benevolent policy-maker in the final Stage 4 is incomplete. Proposition 3 builds a result that is parallel to Proposition 2.

Proof. By Proposition 1, the signal is informative if transfer is prohibitive; hence, (a0∗,a1∗)=(0,1). However, given non-participation, we have (a0,a1)=(1,1). Hence, there is a single distortion at low signal realization, a0≠a0∗.

The interpretation of the welfare loss in this setting is straightforward. The policy-maker faces a tradeoff between the amount of information (public benefits) and the amount of money (private benefits). Since the two types of benefits are weighted one to one and the policy-maker has full bargaining power, the typical scenario is as follows: the policy-maker encourages the disclosure of the privately informed lobby, which maximizes the public benefits. To do so, the policy-maker compensates the lobby for the potential adverse effect of disclosure on the privately informed lobby (i.e. offers a compensation) or exploits the potential beneficial effect of disclosure on the lobby (i.e. requires a fee). The proposed transfer exactly restores the lobby’s outside option. Thus, the policy-maker can both maximize the public benefits and extract part of the public benefits to himself.

However, this scenario does not work if the lobby’s outside option is high and the extra public benefits are low. In such a setting, the compensation is prohibitively costly, and the policy-maker sacrifices increasing the public benefits for savings private costs. Unlike the previous setting with a non-benevolent policy-maker, this setting with a mixed objective yields a genuine tradeoff between the amounts of private and public benefits.

5.1 Preferences regarding information structures

We first derive the partner’s preferences regarding noise (α,β). The preferences depend primarily on the status-quo action:

1. High (favorable) status-quo action, aθ=1: Clearly, the partner prefers an uninformative signal, which implies that the surplus is zero and that the partner defends the high action.

2. Low (unfavorable) status-quo action, aθ=0: For both timings, the partner participates. Hence, the partner always obtains the payoff of her outside option, which is the value of the low action. Thus, the partner is indifferent regarding noise.

The policy-maker’s preferences are given by the maximization of the level of surplus. ^[6]

1. High (favorable) status-quo action, aθ=1, and ex ante access: In Section 3.5, we observed that the shape of the iso-surplus curves depends on the relative valuation: (i) If V≥1, the surplus is maximized at noiseless signal (α,β)=(0,0). (ii) If V<1, then the surplus is maximized at an uninformative signal.

2. Low (unfavorable) status-quo action, aθ=0, or interim access: By inspection of eqs [2] and [3], the iso-surplus curves have the same slope as that identified in Section 3.5. The only difference is that the surplus level is always non-negative because the surplus is monotonic in noise for the informativeness condition. Thus, the maximal surplus depends on the relative valuation: (i) If V≥1, the surplus is maximized at noiseless signal (α,β)=(0,0). (ii) If V<1, then the surplus is maximized in the neighborhood of the biased informative signal (α,β)→(0,1). In this interesting scenario, any incremental transfer from the lobby compensates an incremental policy loss, hence the policy-maker maximizes extraction by maximizing the frequency of the high types.

To sum up, in a standard scenario (V≥1), the objectives of the partner and the policy-maker are exactly opposite. In an alternative scenario (V<1 and aθ=1), both players prefer an uninformative signal and there is no conflict between the policy-maker and the lobby over the information structure.

5.2 Non-skeptic policy-maker

Relaxing the assumption of full disclosure (Assumption 1) has no effect on the equilibrium payoffs as long as we maintain weak dominance.

1. Consider the high type of the lobby. Non-disclosure (d1=0) is weakly dominated by disclosure (d1=1). The posterior belief under disclosure is π1, while the posterior belief under non-disclosure for any mixed-strategy profile lies in the interval [π0,π1]. The lobby’s payoff is increasing step wise in the posterior; hence, the action that maximizes the posterior weakly dominates all other actions.

2. Consider the low type of the lobby. The argument above shows that the high type of the lobby discloses evidence (d1=1) under weak dominance. Thus, the posterior under non-disclosure, for any profile including a mixed-strategy profile, is equal to π0. The posterior under disclosure is also π0. Thus, the policy-maker’s action a remains constant. The low type of the lobby is indifferent regarding any combination of disclosure and non-disclosure.

In contrast, allowing a pooling equilibrium under interim access (i.e. relaxing Assumption 2) may have an effect. The pooling profile is (e1,e2)=(0,0). The posterior belief for non-participation is now πθ, which implies status-quo action aθ. Thus, the outside option (participation condition) of the high type of the lobby is now characterized by the status-quo action, not the low action. As a result, the bargaining surplus for interim access under a pooling profile is

By comparing eqs [14] and [2], we find that Hp(α,β,πθ)=S(α,β,πθ). Since a pooling profile is an equilibrium only if the high type of the lobby does indeed not participate, Hp(α,β,πθ)<0, it exist under interim access if and only if the transfer is prohibitive also under ex ante access. In a word, the existence of a pooling equilibrium eliminates any difference between the interim and ex ante access.