doi: 10.3934/jdg.2018019

Delegation principle for multi-agency games under ex post equilibrium

Department of Economics, University of Graz, Graz, Styria 8010, Austria

Received  July 2017 Revised  April 2018 Published  October 2018

We explore the strategic equivalence between the delegated menu contracting procedure and the centralized mechanism contracting procedure in general pure strategy multi-agency games under ex post equilibrium. We allow information externalities, contract externality, correlated types, and primitive constraints across the contracts for different agents. Our delegation principle identifies that even under this general setting ex post menu design is strategically equivalent to bilateral ex post mechanism design, which simplifies collective ex post mechanism design by ignoring relative information reference. Moreover, one can restrict attention to product menu design problems out of general menu design problems if the contract constraint sets have product structures. We provide conditions for when the principal can do strictly better by using the collective mechanism. Our results still hold if we include individual rationality or any degenerated form of our general model.

Citation: Yu Chen. Delegation principle for multi-agency games under ex post equilibrium. Journal of Dynamics & Games, doi: 10.3934/jdg.2018019
References:
[1]

K. Arrow and G. Debreu, Existence of an equilibrium for a competitive economy, Econometrica, 22 (1954), 265-290. doi: 10.2307/1907353.

[2]

K. Chung and J. Ely, Ex-post incentive compatible mechanism design, Northwestern University Discussion Paper, (2006).

[3]

V. Dequiedt and D. Martimort, Vertical contracting with informational opportunism, American Economic Review, 105 (2015), 2141-2182.

[4]

R. GiammarinoT. Lewis and D. Sappington, An incentive approach to banking regulation, Journal of Finance, 48 (1993), 1523-1542.

[5]

S. Han, Menu theorems for bilateral contracting, Journal of Economic Theory, 131 (2006), 157-178. doi: 10.1016/j.jet.2005.04.002.

[6]

C. Himmelberg, Measurable relations, Fundamenta Mathematicae, 87 (1975), 53-72. doi: 10.4064/fm-87-1-53-72.

[7]

C. HimmelbergT. Parthasarathy and F. Van Vleck, Optimal plans for dynamic programming problems, Mathematical of Operations Research, 1 (1976), 390-394. doi: 10.1287/moor.1.4.390.

[8]

D. Martimort and L. Stole, The Revelation and delegation principles in common agency games, Econometrica, 70 (2002), 1659-1673. doi: 10.1111/1468-0262.t01-1-00345.

[9]

R. McLean and A. Postlewaite, Implementation with interdependent valuations, Theoretical Economics, 10 (2015), 923-952. doi: 10.3982/TE1440.

[10]

P. Monteiro and F. Page, Catalog competition and Nash equilibrium in nonlinear pricing games, Economic Theory, 34 (2008), 503-524. doi: 10.1007/s00199-006-0196-1.

[11]

P. Monteiro and F. Page, Endogenous mechanisms and Nash equilibrium in competitive contracting games, Journal of Mathematical Economics, 45 (2009), 664-678. doi: 10.1016/j.jmateco.2008.05.003.

[12]

F. Page, Mechanism design for general screening problems with moral hazard, Economic Theory, 2 (1992), 265-281. doi: 10.1007/BF01211443.

[13]

F. Page and P. Monteiro, Three principles of competitive nonlinear pricing, Journal of Mathematical Economics, 39 (2003), 63-109. doi: 10.1016/S0304-4068(02)00084-8.

[14]

M. Peters, Common agency and the revelation principle, Econometrica, 69 (2001), 1349-1372.

[15]

J. Rochet, The taxation principle and multi-time Hamilton Jacobi equations, Journal of Mathematical Economics, 14 (1985), 113-128. doi: 10.1016/0304-4068(85)90015-1.

[16]

J. Rosen, Existence and uniqueness of equilibrium points for concave n-person games, Econometrica, 33 (1965), 520-534. doi: 10.2307/1911749.

[17]

A. Tulcea, On pointwise convergence, compactness and equicontinuity in the lifting topology I, Z. Wahrscheinlichkeitstheorie verw. Geb., 26 (1973), 197-205. doi: 10.1007/BF00532722.

show all references

References:
[1]

K. Arrow and G. Debreu, Existence of an equilibrium for a competitive economy, Econometrica, 22 (1954), 265-290. doi: 10.2307/1907353.

[2]

K. Chung and J. Ely, Ex-post incentive compatible mechanism design, Northwestern University Discussion Paper, (2006).

[3]

V. Dequiedt and D. Martimort, Vertical contracting with informational opportunism, American Economic Review, 105 (2015), 2141-2182.

[4]

R. GiammarinoT. Lewis and D. Sappington, An incentive approach to banking regulation, Journal of Finance, 48 (1993), 1523-1542.

[5]

S. Han, Menu theorems for bilateral contracting, Journal of Economic Theory, 131 (2006), 157-178. doi: 10.1016/j.jet.2005.04.002.

[6]

C. Himmelberg, Measurable relations, Fundamenta Mathematicae, 87 (1975), 53-72. doi: 10.4064/fm-87-1-53-72.

[7]

C. HimmelbergT. Parthasarathy and F. Van Vleck, Optimal plans for dynamic programming problems, Mathematical of Operations Research, 1 (1976), 390-394. doi: 10.1287/moor.1.4.390.

[8]

D. Martimort and L. Stole, The Revelation and delegation principles in common agency games, Econometrica, 70 (2002), 1659-1673. doi: 10.1111/1468-0262.t01-1-00345.

[9]

R. McLean and A. Postlewaite, Implementation with interdependent valuations, Theoretical Economics, 10 (2015), 923-952. doi: 10.3982/TE1440.

[10]

P. Monteiro and F. Page, Catalog competition and Nash equilibrium in nonlinear pricing games, Economic Theory, 34 (2008), 503-524. doi: 10.1007/s00199-006-0196-1.

[11]

P. Monteiro and F. Page, Endogenous mechanisms and Nash equilibrium in competitive contracting games, Journal of Mathematical Economics, 45 (2009), 664-678. doi: 10.1016/j.jmateco.2008.05.003.

[12]

F. Page, Mechanism design for general screening problems with moral hazard, Economic Theory, 2 (1992), 265-281. doi: 10.1007/BF01211443.

[13]

F. Page and P. Monteiro, Three principles of competitive nonlinear pricing, Journal of Mathematical Economics, 39 (2003), 63-109. doi: 10.1016/S0304-4068(02)00084-8.

[14]

M. Peters, Common agency and the revelation principle, Econometrica, 69 (2001), 1349-1372.

[15]

J. Rochet, The taxation principle and multi-time Hamilton Jacobi equations, Journal of Mathematical Economics, 14 (1985), 113-128. doi: 10.1016/0304-4068(85)90015-1.

[16]

J. Rosen, Existence and uniqueness of equilibrium points for concave n-person games, Econometrica, 33 (1965), 520-534. doi: 10.2307/1911749.

[17]

A. Tulcea, On pointwise convergence, compactness and equicontinuity in the lifting topology I, Z. Wahrscheinlichkeitstheorie verw. Geb., 26 (1973), 197-205. doi: 10.1007/BF00532722.

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