Political Biases in Lobbying under Asymmetric Information

Political Biases in Lobbying under Asymmetric Information1
David Martimort2 and Aggey Semenov3
This version: 6th September 2006
Abstract: This paper introduces asymmetric information in a pluralistic model of interest
groups competition and analyzes its impact on policy biases. Lobbying groups are
uninformed on a decision-maker’s preferences and use nonlinear contributions not only to
compete for the agent’s services but also to learn about his preferences in an otherwise
standard common agency model of lobbying. Asymmetric information can be, either on
the decision-maker’s ideal point (horizontal differentiation) or on the strength of his own
preferences for ideology (vertical differentiation). At equilibrium, asymmetric information
redistributes bargaining powers between interest groups and the decision-maker in
non-trivial ways that may depend on the kind of informational asymmetry which is postulated.
Asymmetric information tends to mitigate the influence of interest groups and
contributions might be significantly reduced. Interest groups no longer contribute for a
change in policy what it is worth to them as under complete information. Contributions
incorporate a discount related to the group’s ability to solve the asymmetric information
problem.
Keywords: Common Agency, Lobbying Competition, Asymmetric Information.
JEL Classification : D72; D82.
1 Introduction
Two different and somewhat complementary views of how interest groups (thereafter IGs)
influence policy-making prevail nowadays in the economic literature. The first approach
follows what political scientists would coin as being the pluralistic view of politics.4 This
trend of research assumes a priori that some IGs (which have already succeeded in solv-
1This paper was prepared for the EEA 2006 Meeting in Vienna. We thank seminar participants there.
The usual disclaimer applies.
2University of Toulouse, Institut Universitaire de France and EHESS.
3National University of Singapore.
4See Dahl (1961).
1
ing the Olsonian collective action curse) are involved in a hidden gaming whose resulting
equilibrium reflects the power of those existing political forces. Even though earlier contributions
in this line of thought can be traced back to Bentley (1908), it is more deeply
associated to the Chicago School5 and certainly culminated more recently with the work
of Grossman et Helpman (1994) among others. These authors viewed the political game
played by IGs as a common agency game.6 IGs (the principals) influence a decision-maker
(the common agent) by means of contributions which depend on the policy that the latter
chooses. For the so-called “truthful” equilibria of these complete information games, each
IG’s marginal contribution for a policy change reflects his preferences among alternatives.
The resulting equilibrium policy is thus efficient, i.e., it maximizes the aggregate payoff of
the grand-coalition formed of all the existing groups and the decision-maker. The distribution
of the political surplus reflects the political power of the different organized groups
and how the decision-maker can use lobbying competition to pit one group against the
other. In the complete information environment, the power of a group can be roughly
defined as its ability to move policy towards his own ideal point.
The second approach of how interest groups influence policy relies instead on private
information as the engine of influence on the political process. There is no room here to
give full credit to all contributions which describe this informational channel. Grossman
and Helpman (2001) offer an exhaustive presentation of the issues that arises in signalling
models where informed IGs move first and influence decision-makers only by means of
communication. The New Regulatory Economics7 puts also informational asymmetries
and the resulting trade-off between allocative efficiency and rent extraction at the core of
the analysis but stresses also that monetary transfers can be used to mitigate informational
conflicts. Regulatory institutions and contracts respond then to the influence of IGs and
aim at limiting the informational rents that those groups might withdraw from public
decision-making. In this approach, the political power of a group is related to its ability
to secure some informational rent. Indeed, it is a basic lesson of Incentive Theory that
asymmetric information might introduce some bias towards the ideal point of the informed
party.8 Although it helps justifying the forces that create IGs in the first place, this
informational approach somewhat neglects competition among IGs and, by focusing on
an ex ante optimal design of institutions and contracts, it might be viewed by some
scholars as giving too much commitment power to decision-makers. In other words and
to summarize roughly, the weakness of the pluralistic approach corresponds to the strength
of the informational approach and vice versa.
There is certainly still a long way before fully reconciling those two views of the
5See Peltzman (1976) and Becker (1983) among others.
6See Bernheim and Whinston (1986) for a presentation of those games.
7See Laffont and Tirole (1993) among others.
8See Laffont and Martimort (2002) for instance.
2
political process and having a model which simultaneously explains institutional design
and endogenizes groups formation and political biases.9 Although it goes towards this
direction, this short paper should only be viewed as a first exploratory step on this avenue.
In the sequel, we introduce various forms of asymmetric information in an otherwise
standard common agency model of pluralistic politics. The IGs’ monetary contributions
not only have an influence role but are also used as screening devices. This extension of
the basic pluralistic model yields the following insights:
• First, asymmetric information redistributes bargaining powers among IGs and decisionmakers
in non-trivial ways. As such, asymmetric information is an important ingredient
to explain both some systematic biases towards either some IGs or the decision-maker.
• Second, under asymmetric information, IGs no longer contribute for a policy change
what it is worth to them as under complete information but contributions incorporate
a discount related to their ability to solve the asymmetric information problem. This
discount might be so large that some groups may prefer to eschew intervention on DMs
who are too hard to influence. Different groups do not suffer in the same way from paying
this discount and this is reflected in their resulting influence on the political process.10
Section 2 presents the model. In Section 3, we introduce some form of vertical differentiation.
DMs trade off social welfare maximization against the monetary contributions
they receive from IGs. They have the same ideal policy but differ in terms of the weight
they give to ideology which is private information. IGs ignore this weight. The equilibrium
policy may be systematically biased towards the weakest IG, the one whose preferences are
further away from the decision-maker is the policy space. In Section 4, we analyze the case
of horizontal differentiation. Decision-makers differ now in terms of their most preferred
policy and have private information on this parameter. The equilibrium policy might be
systematically biased towards the decision-maker’s ideal point featuring some fundamental
gridlock and status quo bias of economic policy. Contributions are small, sometimes
even null when horizontal uncertainty is large enough. Section 5 offers some synthetic
perspective on the forces that affect political biases under asymmetric information.11
9The ultimate objective of such analysis should be to predict under which legislative organization
some interest groups may be more efficient at intervening than others.
10Using a complete information model of lobbying in the context of import tariffs for intermediate goods,
Gawande and Krishna (2005) argued for instance that the competition between IGs (final producers and
intermediate ones) whose impacts cancel out might explain that the estimated implicit weight given to
contributions in the decision-maker’s preferences is rather low. Asymmetric information would magnify
this bias towards the decision-maker’s ideal point.
11Proofs are relegated to an Appendix.
3
2 The Model
Two IGs (also called principals) P1 and P2 influence a decision-maker (the agent, thereafter
DM) who chooses a policy q in a one dimensional space. P1 has an ideal point located at
a1 = a + b, whereas P2’s ideal point is located at a2 = −a.12 The DM’s ideal point is at
. This ideal point can be viewed as a socially optimal policy when both the well-beings
of unorganized and organized IGs are taken into account. It can also be viewed as the
median voter’s ideal point if the DM’s objectives are aligned with those of voters as a
whole or as an ideological status quo otherwise. The IGs and the DM have quasi-linear
utility functions respectively given by
Vi = −
1
2
(q − ai)2 − ti, for i = 1, 2 and U = −

2
(q − )2 + t1 + t2,
where  is a scale parameter capturing the intensity of DM’s ideological preferences towards
his own ideal point. Contributions ti are non-negative.
Under horizontal asymmetric information, DMs differ in terms of their ideal points
.13 Under vertical asymmetric information, DMs have the same ideal point but differ in
terms of their ideological bias .14
Timing: The lobbying game unfolds as follows. First, both IGs offer non-cooperatively
and commit to contribution schedules ti(q) which stipulate a monetary transfer depending
on the realized policy. Second, the DM decides whose offers to accept (if any) and then
chooses an optimal policy.
Complete Information: The efficient policy q(, ) which maximizes the aggregate
payoff of the grand-coalition formed by both IGs and the DM is a weighted average of
the different player’s ideal points with weights reflecting their ideological biases:
q(, ) =
b + 
2 + 
.
When b > 0, this policy is biased towards P1’s ideal point which is further away from
the DM’s own ideal point than P2’s. Henceforth, we will refer to P1 (resp. P2) as the
weak (resp. strong) principal. Moreover, as  increases, q(, ) comes closer to the
DM’s ideal point reflecting the compromising role of DM’s ideology. From Bernheim and
12We assume a > 0 and b  0.
13That IGs are uninformed on this parameter can be justified when there exists a number of constraints
on the political process that are ignored by those groups. Typical examples would be the slack on the
budget constraint faced by the decision-maker or the strength of unmodeled IGs’ influence. Even when
individuals have been elected on the basis of some ideological platforms, there still remains considerable
uncertainty on their incentives to stick to this platform ex post. To quote Charles Pasqua (a former
French Minister), “Promises only commit those who listen to them”...
14Typically, IGs may have difficulties in figuring out the importance of ideology for a newly appointed
decision-maker.
4
Whinston (1986), this first-best outcome can be implemented through truthful schedules
ti(q) = max{0,−1
2 (q − ai)2 − Ci} i = 1, 2 for some constants (C1,C2) which actually give
the IGs’ equilibrium payoffs.15
3 Vertical Asymmetric Information
The DM has now private information on  but this ideological bias is not too strong; 
is uniformly distributed on [0, ¯ ] for ¯   1. For simplicity, we also assume that  = 0.
Proposition 1 Assume vertical asymmetric information on the DM’s preferences. Then
the equilibrium policy qe() is upward distorted w.r.t. first-best q(0, ):
qe() =
b
2 + 3 − 2 ¯ 
 q(0, ) with equality only at  = ¯ . (1)
The DM always gets a strictly positive payoff in equilibrium. The weak principal’s marginal
contribution is greater than that of the strong principal.
Each IG wants of course to push the policy towards his own ideal point. Absent
the other group’s intervention, this requires a greater (resp. lower) transfer when the
DM has a strong (resp. weak) ideological bias. Under asymmetric information and still
absent the other group’s intervention, a DM with a low ideological bias would thus be
tempted to exaggerate this bias to receive greater compensations from that group.16 This
would call for leaving a positive information rent to DMs having small ideological biases.
When IGs bid instead for favors, both offer large contributions to those DMs. DMs with
stronger ideological biases find it now attractive to pretend having less.17 Because IGs have
opposite preferences, each of those can only mitigate the equilibrium policy that the other
would induce being alone. This makes this policy less sensitive to the DM’s ideological
bias. In other words, the information rent that this DM gets by taking both contracts
is less steep than when taking only one of those and only the  = 0 DM is indifferent
between taking both contributions or only one. To limit the extra rent left to DMs with
stronger ideological biases, both IGs offer contributions which have less mitigating power
compared with what they offer when knowing . This is true for both principals but the
strong one is doing so even more. Indeed, contributions are designed to counter the other
IG’s preferences and the weak IG’s marginal contribution is greater because the strong
15The constants (C1,C2) are obtained by solving a system of equations coming from specifying the
DM’s participation constraints:
P2
i=1 ti(q(, )) − 
2 (q(, ) − )2 = max{0, maxq ti(q) − 
2 (q − )2}.
See also Laussel and Lebreton (2001) on that.
16Incentive constraints are binding upward.
17Incentive constraints are now binding downwards.
5
one is close to the DM in the policy space. At equilibrium, the equilibrium policy is thus
upward distorted for all types  < ¯ .18 Vertical asymmetric information redistributes
somewhat the bargaining power in favor of the weakest IG.19,20
4 Horizontal Asymmetric Information
Let us now turn to the case where  is private information, drawn uniformly on an interval
[−, ]. To simplify, both IGs are symmetrically located around 0, i.e., b = 0. For the
purpose of this paper, we focus on  > 1, i.e., the DM’s ideological preferences are now
sufficiently pronounced.
To understand the impact of horizontal asymmetric information, it is first useful to
think of P1 as being the only IG around. For the moment, let us assume a > , i.e.,
whatever the agent’s ideal point, the IG’s preference is more extreme. Under complete
information, P1 would offer a policy maximizing the aggregate payoff of the bilateral
coalition formed with the agent, i.e., q
1() = a+
1+ . When a > , this policy is always
greater than , i.e., unambiguously biased in the direction of P1’s ideal point. Under
complete information, inducing the agent to adopt this policy requires giving to the DM
a reward t
1() = 
2(1+)2 (a−)2 leaving him just indifferent between the status quo policy
 and choosing q
1(). Of course, this reward is greater for more moderate types.
Under asymmetric information, such scheme is not incentive compatible. More extreme
types who are closer to P1’s own ideal point would like to appear moderate to
grasp those high transfers. To avoid this, P1 increases the distance between the policy
suggested to moderate types and his own ideal point. Reducing the information rent of
extremist DMs calls for distorting the policy in the direction of the agent’s ideal point
and paying less transfer to moderate types. However, P1 is constrained in doing so by the
fact that the DM may always refuse any contribution and choose the status quo policy.
18At equilibrium, everything happens as if the true ideological bias  was replaced by a lower virtual
bias ˜  = 3 − 2 ¯   .
19Lebreton and Salani´e (2003) analyzed a model with the similar features although the sets of possible
policies and contributions are finite. Suppose that the DM has to choose between the IGs’ ideal points.
Efficiency from the grand-coalition’s viewpoint calls for choosing −a since P2’s ideal point is closer to
the agent’s one. Under asymmetric information, assume that Pi only makes a contribution ti when
ai is chosen. Compared with our framework which entails overlapping areas of influence, the lobbying
game is turned into a pure head-to-head competition. The inefficient policy a + b is chosen by the DM
whenever t1 − 
2 (a + b)2  t2 − 
2 a2 i.e., when   2(t1−t2)
b(2a+b) = . The equilibrium contributions are
respectively 1
2 (2a + b)2 − te
1 = b(2a+b)
2  and 1
2 (2a + b)2 − te
2 = b(2a+b)
2 ( ¯  − ). From this, we obtain
 = ¯
3 and te
1 > te
2. The equilibrium under asymmetric information is inefficient with the weak principal
P1’s ideal point being now chosen when   .
20The fact that the IGs are asymmetric (i.e., b > 0) is crucial. Otherwise, the first-best efficient policy
would always be the agent’s ideal point even under asymmetric information (see (1)) and asymmetric
information induces no extra bias.
6
The second-best optimal policy is now defined as:
qe
1() = max

a + (2 − )
1 + 
, 

 q
1(). (2)
The optimal policy in this monopolistic screening environment is thus at least the agent’s
ideal point. It might be distorted upward towards the IG’s ideal point only over the
interval [ −a
−1 , ]. When a  , this interval is empty. Hence, the best-response of P1 to a
null contribution by P2 is itself also null.
Proposition 2 Assume horizontal asymmetric information on the DM’s ideal point with
a   and  > 1. Then, there exists an equilibrium where IGs do not contribute and the
status quo policy qe() =  is implemented.
Asymmetric information undermines significantly the influence of IGs as soon as horizontal
uncertainty is large enough. It is akin to an implicit increase of the DM’s bargaining
power in the political process. Because they are symmetrically located around the agent’s
expected ideal point, none of the IGs gains anything from this bias contrary to the case
of vertical uncertainty.
Under horizontal asymmetric information, different kinds of equilibria may emerge
depending on whether the DM is easily influenced or not and depending on the uncertainty
on his preferences. Martimort and Semenov (2006) describe such equilibria and show that,
as uncertainty on the agent’s type diminishes, IGs may first secure areas with unchallenged
influence, then contributions may overlap for the most moderate types and finally for all
types if uncertainty is very small. The fact that contributions may be null over some range
provides a nice endogenous reasons for why a group fails to intervene on ideologically too
distant DMs.
5 Concluding Remarks
Although they significantly differ in terms of the directions of political biases induced by
asymmetric information, both models above have some common features that we would
like to stress in this concluding section. In both cases, the DM’s type whose allocation
attracts other types would receive the greater contributions had contracting taken place
under complete information. This may be due to the fact that this DM is easily influenced
and IGs competition increases contributions in the first model. This may instead be due to
the fact that the DM is too moderate and hard to move away towards the more extremist
views of IGs in the second model even if those groups secure unchallenged influence.
Asymmetric information and the desire of IGs to reduce the DM’s information rent calls
7
for mitigating the role of IGs, making them less willing to contribute and to influence
those types who are so attractive for others. In both cases, the equilibrium political bias
that results reflects who are the “winners” of the game under asymmetric information,
i.e., those groups or decision-makers who suffer less from it, but in any case, IGs find
influence a much harder job.
References
Becker, G., (1983), “A Theory of Competition Among Pressure Groups for Political Influence”,
Quarterly Journal of Economics, 98: 371-400.
Bentley, A., (1908), The Process of Government, Chicago: Chicago University Press.
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Influence”, Quarterly Journal of Economics, 101: 1-31.
Dahl, R., (1961), Who Governs? Democracy and Power in American City, New Haven:
Yale University Press.
Gawande, K. and P. Krishna, (2005), “Lobbying Competition over U.S. Trade Policy”,
NBER Working Paper No 11371.
Grossman, G. and E. Helpman, (1994), “Protection for Sale”, American Economic Review,
84: 833-850.
Grossman, G. and E. Helpman, (2001), Special Interest Politics, Cambridge: MIT Press.
Laffont, J.J. and D. Martimort, (2002), The Theory of Incentives: The Principal-Agent
Model, Princeton University Press, Princeton.
Laffont, J.J. and J. Tirole, (1993), A Theory of Incentives in Regulation and Procurement,
MIT Press, Cambridge.
Laussel, D. and M. Lebreton, (2001), “Conflict and Cooperation: The Structure of Equilibrium
Payoffs in Common Agency”, Journal of Economic Theory, 100: 93-128.
Lebreton, M. and F. Salani´e, (2003), “Lobbying under Political Uncertainty”, Journal of
Public Economics, 87: 2589-2610.
Martimort, D. and A. Semenov, (2006), “Ideological Uncertainty and Lobbying Competition”,
mimeo IDEI Toulouse.
Martimort, D. and L. Stole, (2005), “On the Robustness of Truthful Equilibria in Common
Agency Games”, mimeo IDEI Toulouse and University of Chicago.
Peltzman, S., (1976), “Towards a More General Theory of Regulation”, Journal of Law
8
and Economics, 19: 211-240.
Seierstad, A. and K. Sydsaeter, (1987), Optimal Control Theory with Economic Applications,
Amsterdam, North Holland.
Appendix
• Proof of Proposition 1: We suppose that P−i offers a non-negative contribution
t−i(q)  0 and look for Pi’s best-response. For ease of notations, denote respectively
Ui() = maxq ti(q) − 
2 q2 and U() = maxq t1(q) + t2(q) − 
2 q2 the agent’s non-negative
information rent when taking only Pi’s contribution and when taking both. Incentive
compatibility yields at any point of differentiability:
˙U
() = −
q2()
2
with ¨U ()  0, (3)
and ˙Ui() = −q2
i ()
2 with ¨Ui()  0 where q() = arg maxq t1(q)+t2(q)− 
2 q2 and qi() =
arg maxq ti(q) − 
2 q2. Pi’s best-response is obtained when solving
(Pi) : max
{q(·),U(·)}
Z ¯
0

−
1
2
(q() − ai)2 −

2
q2() + t−i(q()) − U()

d
subject to (3) and U()  U−i()  0, 8 2 [0, ¯ ]. (4)
As soon as |q−i()| > |q()| 8 2 [0, ¯ ] (a condition to be checked ex post), the participation
constraint (4) is binding only at  = 0. Using U() = U−i(0)−
R 
0
q2(x)
2 dx, inserting
this expression into the maximand of (Pi), integrating by parts and, finally optimizing
pointwise leads to the following necessary FOC:21
−(q() − ai) − q() + t0
−i(q()) = ( − ¯ )q(). (5)
Summing those conditions over i and taking into account that the agent’s choice satisfies P2
i=1 t0
i(q()) = q() yields the equilibrium policy qe() given in (1). It is decreasing
and positive as requested by the SOC in (3). Replacing  by its expression in terms of q
obtained from (1) into (5) yields Pi’s marginal contribution for any q in the range of qe(·):
t0
i(q) = −
(1 − ¯ )
3
q − a−i +
2
3
b, 8i 2 {1, 2}. (6)
These schedules are concave as soon as ¯   1 as assumed. Following Martimort and
Stole (2005), the expression (6) will be extended for any output as long as ti(q)  0.
From (6), we deduce immediately the expression of the policy had the DM refused Pi’s
21It is also sufficient by concavity of the objective as it can be checked ex post once the expression of
the equilibrium schedule t−i(·) is derived.
9
contribution: qi() = 2b−3a−i
3+1−¯ as long as ti(qi())  0.22 Integrating (6), we obtain the
nonlinear equilibrium schedules as
ti(q) = max

0,−
(1 − ¯ )
6
q2 − (a−i −
2
3
b)q − Ci

, 8i 2 {1, 2}. (7)
Observe that t0
1(q) > t0
2(q), capturing the fact that the weak principal contributes more
at the margin than the strongest one’s. The constants (C1,C2) are then determined
by the binding participation constraints at 0: U(0) = U1(0) = U2(0) > 0 which yields
C1 = −18a2+12ab+7b2
12(1−¯) and C2 = −18a2+24ab+b2
12(1−¯) . With those expressions of (C1,C2), one can
easily check that the agent always gets a positive rent for any .
• Proof of Proposition 2: Denote U() = maxq t1(q) − 
2 (q − )2, DM’s non-negative
information rent. Incentive compatibility implies at any point of differentiability:
˙U
() = (q() − ) with ¨U ()  0 (8)
where q() = arg maxq t1(q)− 
2 (q −)2. P1’s best-response to a null contribution offered
by P2 is thus obtained when solving:
(P1) : max
{q(·),U(·)}
Z 
−

−
1
2
(q() − a)2 −

2
(q() − )2 − U()

d
subject to (8) and U()  0 8 2 [−, ]. (9)
The Lagrangean for this optimization problem can be written as:
L(q, U, , μ) = −
1
2
(q − a)2 −

2
(q − )2 − U + (q − ) + μU (10)
where  is the costate variable and μ  0 is the Lagrange multiplier of the pure state
constraint (9). Using the necessary and sufficient conditions for optimality,23 we find
˙
() = 1 − μ() and thus () =  −  − M() for some non-decreasing function M(·)
such that M() = 0. Optimizing pointwise w.r.t. q(·) yields:
−(q() − a) − (q() − ) + ( −  −M()) = 0. (11)
We can now easily guess the candidate solution: μ() = −1
 > 0 (resp. 0) on [−, −a
−1 ]
where qe() =  (resp. [ −a
−1 , ] where qe() = a+(2−)
1+ ).
22Note that q˙i() < 0 as requested by the second-order condition. It is also easily checked that
|q−i()| > |q()| 8 2 [0, ¯ ] so that (4) binds indeed only at 0 and is slack everywhere else.
23See Seierstad and Sydsaeter (1987, Theorem 1, p. 317-319).
10