TY - JOUR
T1 - Virtual Nash implementation with admissible support
AU - Bochet, Olivier
AU - Maniquet, François
N1 - Funding Information:
We thank seminar participants from Universitat Autonoma de Barcelona, University of Rochester, Society for Economic Design Conference, Social Choice and Welfare Conference, GREQAM, Maastricht University and University of Caen for their comments and suggestions. Financial support from Belgium Science Policiy is gratefully acknowledged.
PY - 2010/1/20
Y1 - 2010/1/20
N2 - A social choice correspondence (SCC) is virtually implementable if it is ε-close (in the probability simplex) to some (exactly) implementable correspondence [Abreu, D., Sen, A., 1991. Virtual Implementation in Nash Equilibrium. Econometrica 59, 997-1021] proved that, without restriction on the set of alternatives receiving strictly positive probability at equilibrium, every SCC is virtually implementable in Nash Equilibrium. We study virtual implementation when the supports of equilibrium lotteries are restricted. We provide a necessary and sufficient condition, imposing joint restrictions on SCCs and admissible supports. Next, we discuss how to construct supports, and we underline an important difficulty. Finally, we study virtual implementation when the support is restricted to the efficient or individually rational alternatives.
AB - A social choice correspondence (SCC) is virtually implementable if it is ε-close (in the probability simplex) to some (exactly) implementable correspondence [Abreu, D., Sen, A., 1991. Virtual Implementation in Nash Equilibrium. Econometrica 59, 997-1021] proved that, without restriction on the set of alternatives receiving strictly positive probability at equilibrium, every SCC is virtually implementable in Nash Equilibrium. We study virtual implementation when the supports of equilibrium lotteries are restricted. We provide a necessary and sufficient condition, imposing joint restrictions on SCCs and admissible supports. Next, we discuss how to construct supports, and we underline an important difficulty. Finally, we study virtual implementation when the support is restricted to the efficient or individually rational alternatives.
KW - Admissible support
KW - Extended monotonicity
KW - Maskin monotonicity
KW - Virtual implementation
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U2 - 10.1016/j.jmateco.2009.06.011
DO - 10.1016/j.jmateco.2009.06.011
M3 - Article
AN - SCOPUS:71249144340
SN - 0304-4068
VL - 46
SP - 99
EP - 108
JO - Journal of Mathematical Economics
JF - Journal of Mathematical Economics
IS - 1
ER -