by Ilya Segal
Journal of Economic Theory 2007
The paper examines the communication requirements of social choice rules when
the (sincere) agents privately know their preferences. It shows that for a large class
of choice rules, any minimally informative way to verify that a given alternative is
in the choice rule is by verifying a ìbudget equilibriumî, i.e., that the alternative is
optimal to each agent within a ìbudget setî given to him. Therefore, any communi-
cation mechanism realizing the choice rule must Önd a supporting budget equilibrium.
We characterize the class of choice rules that have this property. Furthermore, for
any rule from the class, we characterize the minimally informative messages (bud-
get equilibria) verifying it. This characterization is used to identify the amount of
communication needed to realize a choice rules, measured with the number of trans-
mitted bits or real variables. Applications include e¢ ciency in convex economies,
exact or approximate surplus maximization in combinatorial auctions, the core in
indivisible-good economies, and stable many-to-one matchings.
2008년 7월 22일 화요일
2008년 7월 5일 토요일
Maskin's Theorem with limited veto power
Games and Economic Behavior, Volume 55, Issue 2, May 2006, Pages 331-339
Jean-Pierre Benoît, Efe A. Ok
Abstract
We weaken the no-veto power condition of Maskin [Maskin, E.,1999. Nash equilibrium and welfare optimality. Rev. Econ. Stud. 66, 23–38] to limited veto power, and prove that any monotonic social choice rule is Nash implementable if it satisfies this weaker condition. The result is obtained by using the canonical Maskin mechanism without modification. An immediate corollary is that the weak core is Nash implementable in any coalitional game environment. An example is given to show that the strong core need not be implementable, even when it is monotonic.
Keywords: Implementation; No-veto power; Core
JEL classification codes: C72; D71
Jean-Pierre Benoît, Efe A. Ok
Abstract
We weaken the no-veto power condition of Maskin [Maskin, E.,1999. Nash equilibrium and welfare optimality. Rev. Econ. Stud. 66, 23–38] to limited veto power, and prove that any monotonic social choice rule is Nash implementable if it satisfies this weaker condition. The result is obtained by using the canonical Maskin mechanism without modification. An immediate corollary is that the weak core is Nash implementable in any coalitional game environment. An example is given to show that the strong core need not be implementable, even when it is monotonic.
Keywords: Implementation; No-veto power; Core
JEL classification codes: C72; D71
A condition guaranteeing that the Nash allocation is Walrasian
A condition guaranteeing that the Nash allocation is Walrasian
David Schmeidler
Abstract
Consider the set of net trades attainable by an economic agent when he varies his strategy and all other agents stick to their strategies. If all attainable sets for all agents are star shaped with respect to the origin, then every Pareto efficient Nash allocation is Walrasian. This result bears upon the question whether it is possible to implement redistributive goals without impairing efficiency.
David Schmeidler
Abstract
Consider the set of net trades attainable by an economic agent when he varies his strategy and all other agents stick to their strategies. If all attainable sets for all agents are star shaped with respect to the origin, then every Pareto efficient Nash allocation is Walrasian. This result bears upon the question whether it is possible to implement redistributive goals without impairing efficiency.
Find Hurwicz's article Naoki mentioned
"On Allocations Attainable through Nash Equilibria", 1979, JET
Journal of Economic Theory, Volume 21, Issue 1, August 1979, Pages 140-165
"On the Dimensional Requirements of Informationally Decentralized Pareto-Satisfactory Processes", 1977, JET
Journal of Economic Theory, Volume 21, Issue 1, August 1979, Pages 140-165
"On the Dimensional Requirements of Informationally Decentralized Pareto-Satisfactory Processes", 1977, JET
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