Common Agency Games Research Articles

“When Olson Meets Dahl”: From Inefficient Groups Formation to Inefficient Policy Making

Two conflicting interest groups buy favor from a policy maker. Influence is modeled as a common-agency game with lobbyists proposing monetary contributions contingent on decisions. When the preferences of the group members are common knowledge, groups form efficiently and lobbying competition perfectly aggregates preferences. When those preferences are instead private information, free riding in collective action arises within groups. Free riding implies that the influence of a group is weakened and that lobbying competition imperfectly aggregates preferences. By softening lobbying competition, private information might also increase groups’ payoffs and hurt the policy maker. Importantly, the magnitudes of informational frictions within each group are jointly determined at equilibrium. We draw from these findings a number of implications for the organization of interest groups.

Complementary Monopolies with asymmetric information

We investigate how asymmetric information on final demand affects strategic interaction between a downstream monopolist and a set of upstream monopolists, who independently produce complementary inputs. We study an intrinsic private common agency game in which each supplier i independently proposes a pricing schedule contract to the assembler, specifying the supplier’s payment as a function of the assembler’s purchase of input i. We provide a necessary and sufficient equilibrium condition. A lot of equilibria satisfy this condition but there is a unique Pareto-undominated Nash equilibrium from the suppliers’ point of view. In this equilibrium, there are unavoidable efficiency losses due to excessively low sales of the good. However, suppliers may be able to limit these distortions by implicitly coordinating on an equilibrium with a rigid (positive) output in bad demand circumstances.

Contracting Sequentially with Multiple Lenders: The Role of Menus

AbstractWe study a credit market in which multiple lenders sequentially offer financing to a single borrower under moral hazard. We show that restricting lenders to post single offers involves a loss of generality: none of the equilibrium outcomes arising in this scenario survives if lenders offer menus of contracts. This result challenges the approach followed in standard models of multiple lending. From a theoretical perspective, we offer new insights on equilibrium robustness in sequential common agency games.

Complementary Monopolies with Asymmetric Information: A Private Common Agency Model

We investigate how asymmetric information on final demand affects strategic interaction between a downstream monopolist and a set of upstream monopolists, who independently produce complementary inputs. We study an intrinsic private common agency game in which each supplier i independently proposes a pricing schedule contract to the assembler, specifying the supplier’s payment as a function of the assembler’s purchase of input i. We provide a necessary and sufficient equilibrium condition. A lot of equilibria satisfy this condition but there is a unique Pareto undominated Nash equilibrium from the suppliers’ point of view. In this equilibrium there are unavoidable efficiency losses due to excessively low sales of the good. However, suppliers may be able to limit these distortions by implicitly coordinating on an equilibrium with a rigid (positive) output in bad demand circumstances.

Does transparency reduce political corruption?

AbstractDoes a better monitoring of officials' actions (transparency) lower the incidence of corruption? Using a common agency game with imperfect information, we show that the answer depends on the measure of corruption that one uses. More transparency lowers the prevalence of corruption but raises the average bribe as it motivates the corruptor to bid more aggressively for the agent's favor. We show that transparency affects the prevalence of corruption at the margin through a competitive effect and an efficiency effect.

On the Role of Menus in Sequential Contracting: A Multiple Lending Example

We study a capital market in which multiple lenders sequentially attempt at financing a single borrower under moral hazard. We show that restricting lenders to post take-it-or-leave-it offers involves a severe loss of generality: none of the equilibrium outcomes arising in this scenario survives if lenders offer menus of contracts. This result challenges the approach followed in standard models of multiple lending. From a theoretical perspective, we offer new insights on equilibrium robustness in sequential common agency games.

Public Contracting in Delegated Agency Games

We study games of public delegated common agency under asymmetric information. Us- ing tools from non-smooth analysis and optimal control, we derive best responses and characterize equilibria (both continuous and discontinuous) using self-generating opti- mization programs of which any equilibrium allocation must be a solution. Special atten- tion is given to common agency games in which each principal’s payoff is a linear function of the agent’s action. In such games the self-generating optimization program reduces to the maximization of the principals’ “aggregate” virtual surplus in which the agent’s marginal valuation is replaced by a confluence of “virtual” valuations that reflect com- mon agency problems. One noteworthy subset of equilibrium allocations are “virtually truthful” which are the incomplete-information generalization of Bernheim and Whin- ston’s (1986) “truthful” equilibria. Virtually-truthful equilibria are simple to calculate and illustrate two distinct sources of equilibrium distortion: inefficient contracting by a given coalition of active principals and inefficient participation (insufficient activity) by principals. Our results are illustrated by means of two games: a public goods game in which each player simultaneously offers a menu contract to a common provider of the public good in order to induce greater supply, and a lobbying game between conflicting interest groups in which each group offers a menu of contributions to a common political decision-maker in an attempt to influence policymaking.

Does Transparency Reduce Corruption?

Does a better monitoring (transparency) of officials lowers the incidence of corruption ? Using a common agency game with imperfect information, we show that the answer depends on the measure of corruption that one uses. More transparency lowers the preval ence of corruption but it may raise the average bribe as it motivates the corruptor to bid more aggressively for the agent’s favour. We show that transparency affects the prevalence of corruption at the margin through a competitive effect and an efficiency effect.

Representing equilibrium aggregates in aggregate games with applications to common agency

An aggregate game is a normal-form game with the property that each playerʼs payoff is a function of only his own strategy and an aggregate of the strategy profile of all players. Such games possess properties that can often yield simple characterizations of equilibrium aggregates without requiring that one solves for the equilibrium strategy profile. When payoffs have a quasi-linear structure and a degree of symmetry, we construct a self-generating maximization program over the space of aggregates with the property that the solution set corresponds to the set of equilibrium aggregates of the original n-player game. We illustrate the value of this approach in common-agency games where the playersʼ strategy space is an infinite-dimensional space of nonlinear contracts. We derive equilibrium existence and characterization theorems for both the adverse selection and moral hazard versions of these games.

Contributing or free-riding? Voluntary participation in a public good economy

We consider a (pure) public goods provision problem with voluntary participation in a quasi-linear economy. We propose a new hybrid solution concept, the free-riding-proof core (FRP-Core), which endogenously determines a contribution group, public good provision level, and its cost-sharing. The FRP-Core is always nonempty in public good economies but does not usually achieve global eciency. The FRP-Core has support from both cooperative and noncooperative games. In particular, it is equivalent to the set of perfectly coalition-proof Nash equilibrium (Bernheim, Peleg, and Whinston, 1987) of a dynamic game with players’ participation decisions followed by a common agency game of public goods provision. We illustrate various properties of the FRPCore with an example. We also show that the equilibrium level of public good shrinks to zero as the economy is replicated.

Lobbying, Regulation in Goods and Labor Markets, and Poisson Technical Change

AbstractI consider an economy in which monopolistic firms produce differentiated products, using skilled and unskilled labor. There is monopolistic competition in the goods market, which determines the size of the rents. There is a self-interested government that determines the minimum wage for unskilled labor, either directly or through the support of labor unions, and the number of firms that can enter the market. Firms devote skilled labor to research and development (R&D) to escape production costs. Interest groups that represent workers and firms lobby the government paying political contributions that are conditional on the government's prospective policy. The labor market is regulated, if the minimum wage is high enough to cause unemployment, and deregulated otherwise.Technically, the model is solved as follows. Monopolistic competition is modeled as a Cournot-Nash game: each firm sets production given the production of the other firms. Because the outcome of R&D in each firm follows a Poisson process, a firm's investment problem is solved by stochastic dynamic programming. The interest groups that represent workers and firms maximize the present value of the workers’ and shareholders’ income, respectively, through their political contributions to the government, while the government maximizes the present value of the political contributions it receives from these. The interest groups act as leaders, but the government as a follower in a common agency game. The outcome of this game determines the government's policy, i.e. the number of firms and the unskilled workers’ minimum wage.The technical contribution of the paper is to show how the Cournot-Nash game, the Poisson technological change due to R&D and the common agency game can be considered within a unifying extended game. The economic prediction of the model is the following. The smaller (greater) the elasticity of substitution between skilled and unskilled labor in production, the more (less) likely there is regulation in the labor market. An increase in the elasticity of substitution between skilled and unskilled labor leads to deregulation in the labor market.

Direct Mechanisms, Menus and Latent Contracts

In common agency games, one cannot characterize all equilibria by considering only direct mechanisms. In an attempt to overcome this difficulty, Peters [Econometrica, 2001] and Martimort and Stole [Econometrica, 2002] identified a class of indirect mechanisms (namely, menus) which are able to characterize every equilibrium. Unfortunately, menus are difficult to handle, and several methodologies have been proposed in the literature. Here, it is shown that, even if authors consider menus rather than simpler mechanisms, many equilibria described in the literature could have been characterized by direct incentive compatible mechanisms. Use of more sophisticated mechanisms was not necessary in these cases.

Truthful Revelation Mechanisms for Simultaneous Common Agency Games

We introduce new revelation mechanisms for simultaneous common agency games which, although they do not always permit a complete equilibrium characterization, do facilitate the characterization of the equilibrium outcomes that are typically of interest in applications. We then show how these mechanisms can be used in applications such as menu auctions, competition in nonlinear tariffs, and moral hazard settings. Lastly, we show how one can enrich the revelation mechanisms, albeit at a cost of an increase in complexity, to characterize all possible equilibrium outcomes, including those sustained by non-Markov strategies and/or mixed-strategy profiles. (JEL C72, D82, D86)

Direct Mechanisms, Menus and Latent Contracts

In common agency games, one cannot characterize all equilibria by considering only direct mechanisms. In an attempt to overcome this difficulty, Peters [1] and Martimort and Stole [2] identi?ed a class of indirect mechanisms (namely, menus) which are able to characterize every equilibrium. Unfortunately, menus are difficult to handle, and several methodologies have been proposed in the literature. Here, it is shown that, even if authors consider menus rather than simpler mechanisms, many equilibria described in the literature could have been characterized by direct incentive compatible mechanisms. Use of more sophisticated mechanisms was not necessary in these cases.

Common agency and public good provision under asymmetric information

The provision of public goods under asymmetric information has most often been viewed as a mechanism design problem under the aegis of an uninformed mediator. This paper focuses on institutional contexts without such a mediator. Contributors privately informed on their willingness to pay non-cooperatively offer contribution schedules to an agent who produces the public good on their behalf. In any separating and informative equilibrium of this common agency game under asymmetric information, instead of reducing marginal contributions to free-ride on others, principals do so to screen the agent's endogenous private information obtained from privately observing other principals' offers. Under weak conditions, the existence of a differentiable equilibrium is shown. Equilibria are always ex post inefficient and interim efficient if and only if the type distribution has a linear inverse hazard rate. This points to the major inefficiency of contribution games under asymmetric information and stands in contrast to the more positive efficiency result that the common agency literature has unveiled when assuming complete information. Extensions of the model address direct contracting between principals, the existence of pooling uninformative equilibria, and the robustness of our findings to the possibility that principals entertain more complex communication with their agent.

Oligopolistic Competition as a Common Agency Game

In applying the common agency framework to the context of an oligopolistic industry, we want to go beyond the classical dichotomy between Cournot and Bertrand competition. We define two games, the oligopolistic game and the corresponding concept of oligopolistic equilibrium, and an associated auxiliary game that can be interpreted as a common agency game and that has the same set of equilibria. The parameterization of the set of (potential) equilibria in terms of competitive toughness is derived from the first order conditions of this auxiliary game. The enforceability of monopolistic competition, of price and quantity competition, and of collusion is examined in this framework. We then describe the (reduced) set of equilibria one would obtain, first in the nonintrinsic case and then in the case where a global approach would be adopted instead of partial equilibrium approach. Finally, we illustrate the use of the concept of oligopolistic equilibrium and of the corresponding parameterization by referring to the standard case of symmetric quadratic utility.

Oligopolistic competition as a common agency game

Oligopolistic competition is analyzed in a complete information multi-principal common agency framework, where principals are firms supplying differentiated goods and the agent is a representative consumer. We first propose a canonical formulation of common agency games, and a parameterization of the set of equilibria based on the Lagrange multipliers associated with the participation and the incentive compatibility constraints of each principal. This is used to characterize the set of equilibria in the intrinsic and non-intrinsic games. The former includes the latter, as well as the standard price and quantity equilibrium outcomes. It may also include the collusive solution.

Selecting equilibria in common agency games

We characterize equilibrium payoffs of a delegated common agency game in a public good context where principals use smooth contribution schedules. We prove that under complete information, payoff vectors of equilibria with truthful schedules coincide with the set of smooth equilibrium payoffs, including non-truthful schedules. We next consider whether the presence of arbitrarily small amounts of asymmetric information is enough to refine this payoff set. Providing that the extensions of the equilibrium schedules beyond the equilibrium point are flatter than truthful schedules, the set of equilibrium payoffs is strictly smaller than the set of smooth (equivalently, truthful) equilibrium payoffs. Interestingly, some forms of asymmetric information do not sufficiently constrain the slopes of the extensions and fail to refine the payoff set. In the case of a uniform distribution of types and arbitrary out-of-equilibrium contributions, the refinement has no bite. If, however, one restricts out-of-equilibrium behavior in a natural way, the refinement is effective. Alternatively, we may consider an exponential distribution with unbounded support (and hence no out-of-equilibrium choices) and we find that the refinement selects a unique equilibrium payoff vector equal to Lindahl prices. As a separate contribution, equilibria with forcing contracts are also considered both under complete and asymmetric information.

Existence of equilibrium in common agency games with adverse selection

We establish the existence of subgame perfect equilibria in general menu games, known to be sufficient to analyze common agency problems. Our main result states that every menu game satisfying enough continuity properties has a subgame perfect equilibrium. Despite the continuity assumptions that we make, discontinuities naturally arise due to the absence, in general, of continuous optimal choices for the agent. Our approach, then, is based on (and generalizes) the existence theorem of [Simon, L., Zame, W., 1990. Discontinuous games and endogenous sharing rules. Econometrica 58 (4), 861–872] designed for discontinuous games.

Existence of Equilibrium in Common Agency Games with Adverse Selection

We establish the existence of sequential equilibria in general menu games, known to be suffcient to analyze common agency problems. In particular, we show that our result solves some unpleasant features of early approaches.