Strategy proofness and unanimity in private good economies with single-peaked preferences

Diss, Mostapha and Doghmi, Ahmed and Tlidi, Abdelmonaim (2015): Strategy proofness and unanimity in private good economies with single-peaked preferences.

Abstract

In this paper we establish the link between strategy-proofness and unanimity in a domain of private good economies with single-peaked preferences. We introduce a new condition and we prove that if this new property together with the requirement of citizen sovereignty are held, a social choice function satisfies strategy-proofness if and only if it is unanimous. As an implication, we show that strategy-proofness and Maskin monotonicity become equivalent. We also give applications to implementation literature: We provide a full characterization for standard Nash implementation and partially honest Nash implementation and we determine a certain equivalence among these theories.

• Item Type: MPRA Paper
• Language: English
• Keywords: Strategy-proofness; Unanimity; Maskin monotonicity, Private goods economies; Single-peaked preferences.
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; D - Microeconomics > D7 - Analysis of Collective Decision-Making; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations

References

[1] K.J. Arrow. Social Choice and Individual Values. 2nd Edition. Wiley, New York,1963.

[2] J.P. Benassy. The Economics of Market Disequilibrium. Academic Press, New York,1982.

[3] D. Black. On the rationale of group decision making. The Journal of PoliticalEconomy, 561:23-34, 1948.

[4] O. Bochet and T. Storcken. Maximal domains for Maskin monotone Pareto optimaland anonymous rules. In: Collective Decision Making: Views from Social Choice and Game Theory (Van Deemen, A. and Rusinowska, A. Eds), Springer, 43:57-68,2010.

[5] W. Bossert and H. Peters. Single-plateaued choice. Mathematical Social Sciences,66:134-139, 2013.

[6] S. Ching. An alternative characterization of the Uniform Rule. Social Choice and Welfare, 11:131-136, 994. [7] G. Demange. Nonmanipulable cores. Economitrica, 55:1057-1074, 1987.

[8] M. Diss, A. Doghmi, and A. Tlidi. Strategy proofness and unanimity in many-to-one matching markets. Working Paper, 2016.

[9] A. Doghmi. A simple necessary condition for partially honest Nash implementation.MPRA Working Paper N 67231, 2015. Available on https://mpra.ub.unimuenchen. de/67231/.

[10] A. Doghmi and A. Ziad. On partially honest Nash implementation in private good economies with restricted domains: A sufficient condition. The B.E.Journal of Theoretical Economics, 13:1-14, 2013.

[11] A. Doghmi and A. Ziad. Nash implementation in private good economies with single-plateaued preferences and in matching problems. Mathematical Social Sciences,73:32-39, 2015.

[12] M. Dummett and R. Farquharson. Stability in voting. Econometrica, 29:33-44, 1961.

[13] B. Dutta and A. Sen. Nash implementation with partially honest individuals. Games and Economic Behavior, 74:154-169, 2012.

[14] A. Gibbard. Manipulation of voting schemes: a general result. Econometrica, 41:587-601, 1973.

[15] M.P. Goswami, M. Mitra, and A. Sen. Strategy proofness and Pareto effeciency in quasilinear exchange economies. Theoretical Economics, 9:361-381, 2014.

[16] M. Hagiwara, H. Yamamura, and T. Yamato. An outcome mechanism for partially honest Nash implementation. Discussion Paper No. 2016-9, 2016.

[17] K. Hashimoto. Strategy-proofness versus effeciency on the Cobb-Douglas domain of exchange economies. Social Choice and Welfare, 31:457-473, 2008.

[18] L. Hurwicz. On informationally decentralized systems. In: Decision and Organization (C. B. McGuire and Roy Radner Eds), pages 297{336, 1972.

[19] N. Kartik, O. Tercieux, and R. Holden. Simple mechanisms and preferences for honesty. Games and Economic Behavior, 83:284-290, 2014.

[20] B. Klaus and O. Bochet. The ralation between monotonicity and strategy-proofness. Social Choice and Welfare, 40:41-63, 2013.

[21] V. Korpela. Bayesian implementation with partially honest individuals. Social Choice and Welfare, 43:647-658, 2014.

[22] M. Lombardi and N. Yoshihara. Partially-honest Nash implementation: A full characterization. MPRA Working Paper No. 48234, ASBS, University of Glasgow,IER, Hitotsubashi University, 2013. Available online at:http://mpra.ub.unimuenchen. de/48234/.

[23] H. Moulin. On strategy-proofness and single peakedness. Public Choice, 35(4):437-455, 1980.

[24] E. Muller and M.A. Satterthwaite. The equivalence of strong positive association and strategy-proofness. Journal of Economic Theory, 14:412-418, 1977.

[25] K. Nehring and C. Puppe. The structure of strategy-proof social choice - Part I: General characterization and possibility results on median spaces. Journal of Economic Theory, 135:269-305, 2007.

[26] J. Ortner. Direct implementation with minimal honest individuals. Games and Economic Behavior, 90:1{16, 2015.

[27] P.K. Pattanaik. Collective rationality of group decision rules. Working Paper No.138, Delhi School of Economics, University of Delhi, August, 1974.

[28] A. Saporiti. Securely implementable social choice rules with partially honest agents. Journal of Economic Theory, 154:2016-228, 2014.

[29] M.A. Satterthwaite. Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory, 10:187-217, 1975.

[30] J. Schummer. Strategy-proofness versus eff eciency on restricted domains of exchange economies. Social Choice and Welfare, 14:47-56, 1997.

[31] T. Sonmez. Strategy-proofness and single-valued cores. Economitrica, 67:677-689,1999.

[32] Y. Sprumont. The division problem with single-peaked preferences: A characterization of the Uniform Rule. Econometrica, 59:509-519, 1991.

[33] H. Yao and J. Yi. Social choice rules implemented in dominant strategies. Economics Letters, 97:197-200, 2007.

[34] L. Zhou. Ineffeciency of strategy-proof allocation mechanisms in pure exchange economies. Social Choice and Welfare, 8:247-254, 1991.