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Dominant Strategy Implementability, Zero Length Cycles, and Affine Maximizers

Author

Listed:
  • Paul H. Edelman

    (Vanderbilt University)

  • John A Weymark

    (Vanderbilt University)

Abstract

Necessary conditions for dominant strategy implementability on a restricted type space are identified for a finite set of alternatives. For any one-person mechanism obtained by fixing the other individuals' types, the geometry of the partition of the type space into subsets that are allocated the same alternative is analyzed using difference set polyhedra. Situations are identified in which it is necessary for all cycle lengths in the corresponding allocation graph to be zero, which is shown to be equivalent to the vertices of the difference sets restricted to normalized type vectors coinciding. For an arbitrary type space, it is also shown that any one-person dominant strategy implementable allocation function (i) can be extended to the unrestricted domain and (ii) that it is the solution to an affine maximization problem

Suggested Citation

  • Paul H. Edelman & John A Weymark, 2017. "Dominant Strategy Implementability, Zero Length Cycles, and Affine Maximizers," Vanderbilt University Department of Economics Working Papers 17-00002, Vanderbilt University Department of Economics.
    • Handle: RePEc:van:wpaper:vuecon-sub-17-00002
    as

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    References listed on IDEAS

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    More about this item

    Keywords

    Dominant strategy incentive compatibility; implementation theory; mechanism design; Roberts' Theorem; Rockafellar--Rochet Theorem;
    All these keywords.

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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