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Individual versus group strategy proofedness: when do they coincide?

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  • Salvador Barberà
  • Dolors Berga
  • Bernardo Moreno

Abstract

A social choice function is group strategy-proof on a domain if no group of agents can manipulate its final outcome to their own benefit by declaring false preferences on that domain. Group strategy-proofness is a very attractive requirement of incentive compatibility. But in many cases it is hard or impossible to find nontrivial social choice functions satisfying even the weakest condition of individual strategy-proofness. However, there are a number of economically signicant domains where interesting rules satisfying individual strategy-proofness can be defi…ned, and for some of them, all these rules turn out to also satisfy the stronger requirement of group strategy-proofness. This is the case, for example, when preferences are single-peaked or single-dipped. In other cases, this equivalence does not hold. We provide sufficient conditions defining domains of preferences guaranteeing that individual and group strategy-proofness are equivalent for all rules defined on these domains. Our results extend to intermediate versions of strategy-proofness, defined to exclude manipulations by small group of agents. They also provide guidelines on how to restrict the ranges of functions defined on domains that only satisfy our condition partially. Finally, we provide a partial answer regarding the necessity of our conditions.

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Bibliographic Info

Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 372.

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Date of creation: Feb 2009
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Handle: RePEc:bge:wpaper:372

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Keywords: strategy-proofness; group strategy-proofness; k-size strategy-proofness; sequential inclusion; single-peaked preferences; single-dipped preferences; separable preferences;

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References

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  1. Saporiti, Alejandro, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
  2. Barbera, Salvador, 1979. "A Note on Group Strategy-Proof Decision Schemes," Econometrica, Econometric Society, vol. 47(3), pages 637-40, May.
  3. Dasgupta, Partha S & Hammond, Peter J & Maskin, Eric S, 1979. "The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 185-216, April.
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  8. Shigehiro Serizawa, 2005. "Pairwise Strategy-Proofness and Self-Enforcing Manipulation," ISER Discussion Paper 0629, Institute of Social and Economic Research, Osaka University.
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  13. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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  15. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
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  17. Peleg, Bezalel, 1998. "Almost all equilibria in dominant strategies are coalition - proof," Economics Letters, Elsevier, vol. 60(2), pages 157-162, August.
  18. Klaus, Bettina, 2001. "Coalitional Strategy-Proofness in Economies with Single-Dipped Preferences and the Assignment of an Indivisible Object," Games and Economic Behavior, Elsevier, vol. 34(1), pages 64-82, January.
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