Menu Auctions and Influence Games with Private Information

Martimort, David; Stole, Lars

doi:10.2139/ssrn.2569703

Cited by 8 publications

(12 citation statements)

References 35 publications

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“…Following a path taken by Martimort and Stole () in their analysis of delegated common agency games, one may select among all equilibria described in Proposition by considering maximization in ( ) over the full domain 𝒬. We denote this output allocation by

q^{m}

, i.e., the unconstrained maximum of the strictly concave objective ( ):

q^{m} false(θ false) \in \underset{q \in normal𝒬}{argmax} S false(q false) - true2.4ex2.4ex(θ + n H false(θ false) true2.4ex2.4ex) q \forall θ \in normalΘ .

The resulting range of optimal outputs in this unconstrained optimization program is also a self‐generating solution to the program in ( ), and so we term it the maximal solution.…”

Section: Characterization Of the Equilibrium Setmentioning

confidence: 99%

“…Under asymmetric information, the distributions of equilibrium payoffs can no longer be disentangled from the allocative distortions that arise at equilibrium. Martimort and Stole () present necessary conditions that are satisfied by all equilibrium outcomes of a delegated public common agency game. Compared with the intrinsic counterpart, delegated public common agency games allow the agent to refuse any strict subset of the principals' offers if he wishes so.…”

Section: Introductionmentioning

confidence: 99%

“…Compared with the intrinsic counterpart, delegated public common agency games allow the agent to refuse any strict subset of the principals' offers if he wishes so. Martimort and Stole () derive maximal equilibria in those contexts and observe that they differ from maximal equilibria in intrinsic games because these additional strategic possibilities require that tariffs must remain nonnegative. The necessary conditions in Martimort and Stole () remain compact enough to describe both continuous and discontinuous equilibrium allocations just as in the intrinsic scenario that is our focus hereafter.…”

Section: Introductionmentioning

confidence: 99%

“…None of these papers investigates the full set of equilibria as we do here. This step is possible by building on techniques similar to those in Martimort and Stole () but now specialized to intrinsic common agency games. Laussel and Resende () also tackle this problem in the specific context of competing manufacturers.…”

Section: Introductionmentioning

confidence: 99%

“… While we use the same notion of maximal solutions in Martimort and Stole () as in the present paper, note that the virtual surpluses in the SGM program of the delegated agency setting of Martimort and Stole () and in the present paper are different. In particular, the space of contracts in the intrinsic common agency game is larger than in the delegated scenario since the latter only includes nonnegative tariffs. …”

mentioning

confidence: 99%

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A complete characterization of equilibria in an intrinsic common agency screening game

Martimort¹,

Semenov²,

Stole

2018

Theoretical Economics

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We characterize the complete set of equilibrium allocations to an intrinsic common agency screening game as the set of solutions to self-generating optimization programs. We provide a complete characterization of equilibrium outcomes for regular environments by relying on techniques developed elsewhere for aggregate games and for the mechanism design delegation literature. The set of equilibria includes those with nondifferentiable payoffs and discontinuous choices, as well as equilibria that are smooth and continuous in types. We identify one equilibrium, the maximal equilibrium, which is the unique solution to a selfgenerating optimization program with the largest (or "maximal") domain, and the only equilibrium that is supported with biconjugate (i.e., least-concave) tariffs. The maximal equilibrium exhibits a n-fold distortion caused by each of the n principal's non-cooperative behavior in overharvesting the agent's information rent. Furthermore, in any equilibrium, over any interval of types in which there is full separation, the agent's equilibrium action corresponds to the allocation in the maximal equilibrium. Under reasonable conditions, the maximal equilibrium maximizes the agent's information rent within the class of equilibrium allocations. When the principals' most-preferred equilibrium allocation differs from the maximal equilibrium, we demonstrate that the agent's choice function exhibits an interval of bunching over the worst agent types, and elsewhere corresponds to the maximal allocation. The optimal region of bunching trades off the principals' desire to constrain inefficient n-fold marginalizations of the agent's rent against the inefficiency of pooling agent types.

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q^{m}

, i.e., the unconstrained maximum of the strictly concave objective ( ):

q^{m} false(θ false) \in \underset{q \in normal𝒬}{argmax} S false(q false) - true2.4ex2.4ex(θ + n H false(θ false) true2.4ex2.4ex) q \forall θ \in normalΘ .

The resulting range of optimal outputs in this unconstrained optimization program is also a self‐generating solution to the program in ( ), and so we term it the maximal solution.…”

Section: Characterization Of the Equilibrium Setmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

A complete characterization of equilibria in an intrinsic common agency screening game

Martimort¹,

Semenov²,

Stole

2018

Theoretical Economics

Self Cite

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Complementary Monopolies with asymmetric information

Laussel

Resende

2019

Econ Theory

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We investigate how asymmetric information on …nal demand a¤ects 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 su¢ cient 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 e¢ ciency 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.

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Reform for Sale

Lefebvre

Martimort

2023

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Lobbying competition is viewed as a delegated common agency game under moral hazard. Several interest groups try to influence a policy-maker who exerts effort to increase the probability that a reform be implemented. With no restriction on the space of contribution schedules, all equilibria perfectly reflect the principals' preferences over alternatives. As a result, lobbying competition reaches efficiency. Unfortunately, such equilibria require that the policy-maker pays an interest group when the latter is hurt by the reform. When payments remain non-negative, inducing effort requires leaving a moral hazard rent to the decision maker. Contributions schedules no longer reflect the principals' preferences, and the unique equilibrium is inefficient. Free-riding across congruent groups arises and the set of groups active at equilibrium is endogenously derived. Allocative efficiency and redistribution of the aggregate surplus is linked altogether and both depend on the set of active principals, as well as on the group size.

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Menu Auctions and Influence Games with Private Information

Cited by 8 publications

References 35 publications

A complete characterization of equilibria in an intrinsic common agency screening game

A complete characterization of equilibria in an intrinsic common agency screening game

Complementary Monopolies with asymmetric information

Reform for Sale

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