, Other approaches have modified the rationality notion, using "partial honesty

, A classic literature considers sequential voting by veto with many players (see Mueller, 1978.

. Moulin, Felsenthal and Machover [1992] and Anbarci [2006]) where each player is assigned a certain number of vetoes to be distributed freely among the alternatives. See also the rules of k-names in Barberà and Coelho, 1981.

]. and L. , See also Jackson and Sonnenschein [2007] who show that linking decisions (that is, a common decision on several independent problems) can help overcoming incentive constraints in References D. Abreu and A. Sen. Virtual implementation in Nash equilibrium, Econometrica, vol.59, issue.4, pp.997-1021, 1991.

N. Anbarci, Finite alternating-move arbitration schemes and the equal area solution, Theory and Decision, vol.61, issue.1, pp.21-50, 2006.

S. Barberà and D. Coelho, On the rule of k-names, Games and Economic Behaviour, vol.70, pp.44-61, 2010.

S. Barberà and D. Coelho, On the Selection of Compromise Arbitrators. mimeo, UAB, 2019.

J. Benoît and E. A. Ok, Nash implementation without no-veto power, Games and Economic Behavior, vol.64, issue.1, pp.51-67, 2008.

D. Bloom and C. Cavanagh, An analysis of the selection of arbitrators, American Economic Review, vol.76, issue.3, pp.408-430, 1986.

O. Bochet, Nash implementation with lottery mechanisms, Social Choice and Welfare, vol.28, issue.1, pp.111-125, 2007.

O. Bochet and F. Maniquet, Virtual Nash implementation with admissible support, Journal of Mathematical Economics, vol.46, issue.1, pp.99-108, 2010.

A. Bogomolnaia and H. Moulin, A new solution to the random assignment problem, Journal of Economic Theory, vol.100, issue.2, pp.295-328, 2001.

T. Börgers and P. Postl, Efficient Compromising, Journal of Economic Theory, vol.144, pp.2057-2076, 2009.

J. Busetto and R. Colognato, Reconsidering Two-Agent Nash Implementation, Social Choice and Welfare, vol.32, pp.171-179, 2009.

J. Chan, A. Lizzeri, W. Suen, and L. Yariv, Deliberating collective decisions. The Review of Economic Studies, vol.85, pp.929-963, 2017.

G. De-clippel, K. Eliaz, and B. Knight, On the selection of arbitrators, American Economic Review, vol.104, pp.3434-58, 2014.

B. Dutta, Recent results on implementation with complete information, Social Design, pp.249-260, 2019.

B. Dutta and A. Sen, A Necessary and sufficient condition for two-person Nash implementation, Review of Economic Studies, vol.58, pp.121-128, 1991.

B. Dutta and A. Sen, Nash Implementation with Partially Honest Individuals, Games and Economic Behavior, vol.74, pp.154-169, 2012.

F. Ederer, R. Holden, and M. Meyer, Gaming and strategic opacity in incentive provision, RAND Journal of Economics, vol.49, issue.4, pp.819-854, 2018.

S. D. Felsenthal and M. Machover, Sequential voting by veto: making the Mueller-Moulin algorithm more versatile, Theory and Decision, vol.33, issue.3, pp.223-240, 1992.

D. Fudenberg and D. K. Levine, Whither game theory? towards a theory of learning in games, Journal of Economic Perspectives, vol.30, issue.4, pp.151-70, 2016.

P. Gärdenfors, Manipulation of social choice functions, Journal of Economic Theory, vol.13, issue.2, pp.217-228, 1976.

M. J. Herrero and S. Srivastava, Implementation via backward induction, Journal of Economic Theory, vol.56, issue.1, pp.70-88, 1992.

L. Hurwicz and D. Schmeidler, Construction of outcome functions guaranteeing existence and Pareto optimality of Nash equilibria, Econometrica, vol.46, pp.1447-1474, 1978.

M. O. Jackson, A Crash Course in Implementation Theory, Social Choice and Welfare, vol.18, pp.655-708, 2001.

M. O. Jackson and H. F. Sonnenschein, Overcoming incentive constraints by linking decisions, Econometrica, vol.75, issue.1, pp.241-257, 2007.

J. Kelly, Strategy-proofness and social choice functions without singlevaluedness, Econometrica, vol.45, issue.2, pp.439-446, 1977.

J. Laslier, M. Núñez, and C. Pimienta, Reaching consensus through approval bargaining, Games and Economic Behavior, vol.104, pp.241-251, 2017.
URL : https://hal.archives-ouvertes.fr/halshs-01630037

E. Maskin, Nash equilibrium and welfare optimality, Review of Economic Studies, vol.66, pp.23-38, 1999.

H. Matsushima, A new approach to the implementation problem, Journal of Economic Theory, vol.45, issue.1, pp.128-144, 1988.

C. Mezzetti and L. Renou, Implementation in mixed Nash equilibrium, Journal of Economic Theory, vol.147, issue.6, pp.2357-2375, 2012.

J. Moore and R. Repullo, Subgame perfect implementation, Econometrica, vol.96, issue.5, pp.1191-1220, 1988.

J. Moore and R. Repullo, Nash implementation: A full characterization, Econometrica, vol.58, pp.1083-1099, 1990.

H. Moulin, Prudence versus sophistication in voting strategy, Journal of Economic theory, vol.24, issue.3, pp.398-412, 1981.

H. Moulin, The strategy of social choice, 1983.

D. C. Mueller, Voting by veto, Journal of Public Economics, vol.10, issue.1, pp.57-75, 1978.

M. Núñez and J. Laslier, Bargaining through approval, Journal of Mathematical Economics, vol.60, pp.63-73, 2015.

M. R. Sanver, Nash implementing non-monotonic social choice rules by awards, Economic Theory, vol.28, issue.2, pp.453-460, 2006.

M. R. Sanver, Implementing Pareto optimal and individually rational outcomes by veto. Group Decision and Negotiation, vol.27, pp.223-233, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02093118