# Baron (2001) - Theories of Strategic Nonmarket Participation

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Has article title | Theories of Strategic Nonmarket Participation |

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- This page is part of a series under PHDBA279A
- This page is referenced in BPP Field Exam Papers

## Reference(s)

Source:

- Baron, D. (2001), Theories of Strategic Nonmarket Participation: Majority-Rule and Executive Institutions, Journal of Economics and Management Strategy 10, 7-45. pdf
- Baron, D. (1999), Theories of Strategic Nonmarket Participation: Majority-Rule and Executive Institutions, Working Paper pdf

Uses:

## Introduction

Baron (2001) provides some theoretical foundations for client politics and interest group politics in both Majority Rule institutions and executive institutions. The paper focuses on complete information settings and does not explicitly consider re-election, though it is noted that contributions are likely to be used to this end.

The models considered are:

**Vote recruitment in client politics (with majority rule institutions)**- Extension to supermajority rule
- Extension to bicameral legislatures
- Extension to presidential veto

- Agenda setting strategies and vote recruitment in client politics
- Extension to consider uncertainty over the location of ideal points
- Extension to consider uncertainty over the intensity of preferences

- Analysis of Bargaining Power in interest group politics
- Analysis of incentive to undertake nonmarket strategies in client/interest group politics
- Forming coalitions for vote recruitment in client politics (cost sharing)
- Rent chain mobilization in client politics
**Interest group competition with an executive institution**- Interest group competition in a majority rule institution
- Vote Recruitment
- Agenda Setting

## Basic Definitions

- In
**Client politics**the firm or interest group has no direct competition in its lobbying or influencing efforts. - In
**Interest group politics**one or more firms directly compete in their efforts to influence policy (note that client politics is a subset of interest group politics, but we will use the term interest group politics to discuss the case of multiple lobbyists). **Majority Rule institutions**are legislatures or similar bodies that who require a majority vote to pass legislation. Thus Majority Rule institutions are synonymous with median vote type problems.**Executive institutions**are those in which a single individual, or a group of individuals that hare identical preference and so can be represented by a single representative agent, are empowered to choose and enact policy.

## Majority Rule Institutions

Key to the analysis of Majority Rule institutions is the notion of **pivotal legislators**, and the trade-off between **costs and benefits** for the lobbyist(s). Building a majority is inherently costly, and so majority building naturally focuses on the legislators who are easiest to recruit. Legislators who would vote to support a policy absent of lobbying efforts are not provided with additional (costly) resources.

## Interest Group Politics

How competition among interest groups should be modelled (to reflect reality) depends four main factors: the **sequence or simultaneity** of offers, whether lobbyists can make more than one offer or not (i.e. the **number of rounds**), the nature of the offers (i.e. **point or menu offers**), and the **number of offers accepted** (generally one or all) . The bullets below give the appropriate model for some of these instances:

- Simultaneous, 1 round, point offers, 1 accepted: Colonel Blotto type games
- Sequential move, point offers, 1 accepted: Groseclose & Synder, Groseclose & Banks.
- Simultaneous, 1 round, 1 accepted, point offers: All pay auctions
- Simultaneous, 1 round, 1 accepted, menu offers: Common agency models, e.g.
**Grossman & Helpman (1994)**

In the last case it should be stressed that **resource offers by the principals are specified as a function of the decision my the agent**.

## Vote Recruitment in Client Politics

A slightly simplified version of the model used now follows.

### Legislators and Interests

Legislators have ideal points: [math]z \backsim U \left [ - \frac{1}{2},\frac{1}{2} \right ][/math] with the median legislator's ideal point denoted [math]\, z_m = 0[/math].

The utility function of legislators is additively-seperable with a term representing their constituent's preferences and a term for the resources provided to them by the client:

- [math]\quad U \left( w , z \right ) = -\alpha(w-z) + r_w, \quad \alpha\gt 0[/math] where [math]\, \alpha[/math] represents the intensity of preferences.

The Interest seeks [math]x \gt 0,\quad x \ge y[/math] where [math]\, y[/math] is the status quo and the Agenda is [math]\, A=\{x,y\}[/math].

A necessary condition for nonmarket action is that [math]\frac{(x+y)}{2} \gt z_m \,[/math]. We can also consider the indifferent voter [math]z_i[/math] and note that this votes will be inactive if [math]z_i \le z_m [/math] and active if [math]\, z_i \gt z_m[/math].

### Resource Provision

A legislator has an absolute-value policy plus resource contribution based utility function. That is a legislator will vote for [math]x[/math] over [math]y[/math] iif:

- [math]-\alpha \left|x-z\right| + r_x \ge -\alpha \left|y-z\right| \qquad[/math] - equation (1)

Note that a legislator votes on his (using male for the agent) induced preferences, not on whether they are pivotal. However, in equilibrium the pivotal votes are recruited.

The resources that must be provided to a legislator to swing his vote (essentially [math]U(y,z)-U(x,z)[/math]) are calculated according to equation (1) above for three different cases (locations of z).

- Case 1: [math]z \le y: \quad r_x=\alpha (x-y)[/math] obtained by noting that [math]x \ge y[/math] and that both of the absolute values are positive and rearranging.

- Case 2: [math]y \le z \le x: \quad r_x= 2 \alpha \left (\frac{x+y}{2} - z \right )[/math] obtained by noting that the LHS absolute value in equation (1) is positive, whereas the RHS value is negative.

- Case 3: [math]x \le z: \quad r_x=-\alpha (x-y)[/math] obtained by noting that both of the absolute values are negative and rearranging.

### Making Legislators Indifferent

For simplicity consider the case where [math]z_m \lt y \lt \frac{x+y}{2} [/math]. Putting these points on a line divides the line into four regions. The resource provision required to make a legislator indifferent in each region is:

- [math]z \in [-\infty,z_m]\,, \quad r^*=0[/math]

- [math]z \in (z_m,y]\,, \quad r^*=\alpha (x-y)[/math]

- [math]z \in (y,\frac{x+y}{2}]\,, \quad r^*=2 \alpha \left (\frac{x+y}{2} - z \right )[/math]

- [math]z \in (\frac{x+y}{2},\infty]\,, \quad r^*=0[/math]

Note that the legislators with ideal points [math]z_m \gt \frac{x+y}{2}[/math] always vote for the interest's policy and there is no need to contribute resources to them. Likewise in it unnecessary to contribute to legislators below the median, at least if there is no uncertainty of types and a majority rule is in place (etc). Further more the resources needed are decreasing in [math]z[/math] for [math]z \in (z_m,\frac{x+y}{2}][/math], so interests must provide more resources to more strongly opposed legislators, and are strictly increasing in [math]x[/math].

### Total Resources

The total resources required are:

- [math]R = \int_0^{\frac{x+y}{2}} r^*[/math]

In the case where [math]y \gt 0\,[/math]:

- [math]\quad r^*=\frac{\alpha}{4}\left ( x+y \right )^2 - \alpha y^2[/math]

In the case where [math]y \le 0\,[/math]:

- [math] \quad r^*=\frac{\alpha}{4}\left ( x+y \right )^2[/math]

### Recruiting Votes

Now suppose that the interest has a utility function described by:

- [math]U_g(w,z_g) = =\beta (w - z_g)^2 -R(x,y)\,, \quad[/math]

where[math]z_g \ge x\,[/math] is the interest's ideal point and [math]\beta \gt 0\,[/math] is the strength of the interest's preferences.

For [math]y \le 0\,[/math], the interest will recruit votes iff:

- [math]-\Beta (x - z_g)^2 - \frac{\alpha}{4}\left ( x+y \right )^2 \ge \beta (y - z_g)^2[/math]

- Or: [math]z_g \ge z_g^-(x,y) \equiv \frac{x+y}{2} \left (1+\frac{\alpha(x+y)^2}{4 \beta (x-y)}\right)[/math]

Therefore if the agenda is exogenous, the interest will recruit if and only if [math]z_g[/math] is to the right of the midpoint by the recruitment factor [math]\frac{\alpha(x+y)^2}{4 \beta (x-y)}[/math]; that is the interest must be extreme in its interests by this factor to undertake recruitment.

This implies that interests that are moderate or centralist (defining centralist as interests whose preferred policy fall in the range [math]z_g \in [0,z_g^-(x,y)]\,[/math]) will not act, leading to inertia in policies.

Likewise one can calculate the upper limit of the range [math]z_g^+\,[/math] for when [math]y \gt 0\,[/math]. The interest will then recruit votes iff:

- [math]z_g \ge z_g^+(x,y) \equiv \frac{x+y}{2} \left (1+\frac{\alpha(x+y)^2}{4 \beta (x-y)}\right) - \frac{\alpha y^2}{2 \beta (x-y)}[/math]

### Comparative Statics

A crucial contribution of this model is that it allows some basic comparative statics. Examination of the effects of changes in exogenous parameters for the case where [math]y \le 0\,[/math] shows that:

- [math]z_g^-(x,y)\,[/math] is strictly decreasing in [math]\beta\,[/math]: With more intense interests there is a smaller centralist set.

- [math]z_g^-(x,y)\,[/math] is strictly increasing in [math]\alpha\,[/math]: With more intense legislator preferences there is a larger centralist set.

- [math]z_g^-(x,y)\,[/math] is strictly increasing in [math]x\,[/math]: A more extreme alternative leads moderate interests not to try to change the policy.

Also as [math]x \uparrow[/math] the #votes recruited [math]\downarrow[/math], and as [math]x \uparrow[/math] the cost of recruiting a vote [math]\uparrow[/math].

It is also possible to calculate when vote recruitment becomes too costly all together for the interest. This is covered in some detail in the paper, but loosely if [math]x \gt x^*(z_g,0)=\frac{8 \beta z_g}{4 \beta + \alpha}\,[/math], then the cost exceeds the gain.

## Interest group competition with an executive institution

The following model is essential a two principal (the "Interests"), single agent (the "Executive"), common knowledge agency model. It is a direct application of the Bernheim and Whinston (1986) model, as implemented by Grossman and Helpman (1994).

### Interests (Principals) and the Executive (Agent)

There are two interests [math]j = \{g,h\}\,[/math] with ideal points [math]z_g \gt 0, \, z_h \lt 0[/math] and support costs [math]c_j(x)\,[/math]. The interests have additively seperable utility functions with an intensity factor [math]\beta_j\,[/math]:

- [math]U_j=u_j(x)-c_j(x) \quad[/math] where [math]u_j(x)=-\beta_j(x-z_j)^2\;\,\beta_j\gt 0[/math]

The executive choses a policy [math]x \in \mathbb{R}\,[/math] and has an additively seperable utility function:

- [math]U_e=u_e(x)+c_g(x)+c_h(x)\quad[/math]where [math]u_e(x)\,[/math] represents the executives own policy preferences.

The status quo policy is taken to be [math]x\gt 0\,[/math] and the sequence of the game is a simultaneous move on support schedules by the principals followed by a choice of policy by the executive. The principals make menu offers, that is they state a resource contribution for each potential policy outcome, and these offers are binding. Once the executive has made the policy choice the contributions are transfered from the principals according the menu value of the chosen policy.

It should be noted that as a result of additive seperability in the utility functions with respect to the contributions, and that both principal(s) and agent value the seperable contribution identically, the contributions are transfers and the agent will maximize the joint surplus - this is proved below. Having two principals introduces competition which favors the agent in an enter/don't enter prisoner's dilemma game that occurs before this game and allows the agent to extract rents from both principals; however, we could correctly determing the outcome of this game by using a single representative principal whose utility function is the sum of the two principals, and then computing a standard principal-agent model.

### Conditions for an SPNE

Baron (or Rui) define equilibrium as a triple [math]c_{g}^{\ast}(x), c_{h}^{\ast}(x), x^{\ast})[/math] is defined as:

- [math]x^{\ast}\in\arg\max_{x}[u_{e}(x)+c_{g}^{\ast}(x)+c_{h}^{\ast}(x)][/math].
- [math]c_{j}^{\ast}\in\arg\max_{c_{j}}[-\beta[x^{\ast}-z_{j}]^{2}-c_{j}^{\ast}(x^{\ast})]m j=g,h[/math].
- [math]c_{j}=\tau_{j}+u_{j}(x), j=h,g[/math], "Truth Telling."

Bernheim and Whinston (1984) provide four necessary and sufficient conditions for a sub-game perfect Nash equilibrium in this model. In the notion of the model, these are:

[math]\{c_j^*(x),x\}[/math] is an SPNE iff:

- a) [math]c_j^*(x)\,[/math] is feasible
- b) [math]x^*\,[/math]maximizes[math]\quad u_e(x) + c_g^*(x) + c_h^*(x)[/math]
- c) [math]\forall j (i \ne j) x^*\,[/math]maximizes [math] \quad \{u_e(x) + c_j^*(x) + c_i^*(x)\} + \{u_j(x) - c_j^*(x)\} = \{u_e(x) + u_j(x) + c_i^*(x)\} [/math]
- d) [math]\forall j (i \ne j) \exists x_j\,[/math]s.t.[math]\quad u_e(x)+c_j^*(x)+c_i^*(x)\;[/math] where [math]c_J^*(x) = 0 \quad \therefore x_j\,[/math] maxes [math]\quad u_e(x) + c_i^*(x)\;[/math]

### Local Truth Telling

The first order conditions of (b) and (c) taken together imply:

- [math]c_J^*\prime(x^*) = u_J^*\prime(x^*)\quad[/math]and therefore that the contribution schedules are locally truthful around [math]x^*[/math].

### Linear Contribution Schedules

The contribution schedules are constructed as linear functions of the utility of the principals, specifically:

- [math]c_J^\tau(x,\tau_j) = max\{0,u_j(x) + \tau_j\}\quad[/math] Note that the linear term is added not subtracted, but that it may be negative.

### Joint Surplus Maximization

The principal's utility maximization and conditions (a) and (b) imply:

- [math]U_e(x^*) \ge U_e(x) \quad \forall x \in \mathbb{R}[/math]
- [math]u_e(x^*) + c_g^*(x^*) + c_h^*(x^*) \ge u_e(x) + c_g^*(x) + c_h^*(x) \quad\forall x \in \mathbb{R}[/math]

When both agents contribute we can substitute in the linear contribution schedules to get:

- [math]u_e(x^*) + u_g^*(x^*) + \tau_g + u_h^*(x^*) + \tau_h \ge u_e(x) + u_g^*(x) + \tau_g + u_h^*(x) + \tau_h \quad \forall x \in \mathbb{R}[/math]
- [math]\therefore u_e(x^*) + u_g^*(x^*) + u_h^*(x^*) \ge u_e(x) + u_g^*(x) + u_h^*(x) \quad \forall x \in \mathbb{R}[/math]

As [math]\widehat{U_e}(x) = u_e(x) + u_g(x) + u_h(x) \quad[/math], the principal's problem is to maximize the joint surplus.

### Solving For Linear Contribution Terms

Using (d) we can note that if player [math]i[/math] doesn't contribute then the agent choses:

- [math]x_j \in \arg \max u_e(x) + u_j(x)\quad[/math]

Comparing this to the equilibrium where both players contribute and noting that for the agent [math]x^* \succsim x_g\,[/math] and [math]x^* \succsim x_h\;[/math], and so it must be the case that [math]x_g , x_h\,[/math] are off the equilibrium path.

Therefore the agent will choose [math]x^*\,[/math] iff:

- [math]u_e(x^*) + c_g^*(x^*) + c_h^*(x^*) \ge u_e(x_g) + c_g^*(x_g) \quad[/math] and likewise for [math]h[/math]

We can solve for the other player's [math]\tau[/math] by setting the inequality exact:

- [math]u_e(x^*) + c_g^*(x^*) + c_h^*(x^*) = u_e(x_g) + c_g^*(x_g) \,[/math]
- [math]u_e(x^*) + u_g^*(x^*) + u_h^*(x^*) + \tau_g + \tau_h = u_e(x_g) + u_g^*(x_g) + \tau_g\,[/math]
- [math]u_e(x^*) + u_g^*(x^*) + u_h^*(x^*) + \tau_h = u_e(x_g) + u_g^*(x_g)\,[/math]
- [math] \tau_h = u_e(x_g) + u_g^*(x_g) - (u_e(x^*) + u_g^*(x^*) + u_h^*(x^*) )\,[/math]

Likewise:

- [math] \tau_g = u_e(x_h) + u_h^*(x_h) - (u_e(x^*) + u_g^*(x^*) + u_h^*(x^*) )\,[/math]

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