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Dominant strategy implementation with a convex product space of valuations

机译：具有凸出估值空间的主导策略实施

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摘要

A necessary and sufficient condition for dominant strategy implementability when preferences are quasilinear is that, for every individual i and every choice of the types of the other individuals, all k-cycles in i’s allocation graph have nonnegative length for every integer k ≥ 2. Saks and Yu (Proceedings of the 6th ACM conference on electronic commerce (EC’05), pp 286–293, 2005) have shown that when the number of outcomes is finite and i’s valuation type space is convex, nonnegativity of the length of all 2-cycles is sufficient for the nonnegativity of the length of all k-cycles. In this article, it is shown that if each individual’s valuation type space is a full-dimensional convex product space and a mild domain regularity condition is satisfied, then (i) the nonnegativity of all 2-cycles implies that all k-cycles have zero length and (ii) all 2-cycles having zero length is necessary and sufficient for dominant strategy implementability.
机译：当偏好为准线性时，占主导地位的策略可实施性的充要条件是，对于每个个体i和其他个体类型的每种选择，i的分配图中的所有k环对于每个k≥2的整数都是非负长度。和Yu（第六届ACM电子商务会议论文集（EC'05），第286-293页，2005年）表明，当结果数有限且i的估值类型空间是凸的时，所有2的长度都是非负的-周期对于所有k周期的长度的非负数是足够的。本文表明，如果每个人的评估类型空间是一维凸产品空间，并且满足温和的域正则条件，则（i）所有2个周期的非负性意味着所有k个周期都为零（ii）具有零长度的所有2个周期对于主导策略的可实施性是必要和充分的。

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  • 来源
    《Social Choice and Welfare》 |2012年第3期|567-597|共31页
  • 作者

    Katherine Cuff; Sunghoon Hong; Jesse A. Schwartz; Quan Wen; John A. Weymark;

  • 作者单位

    Department of Economics McMaster University 1280 Main Street West Hamilton ON L8S 4M4 Canada;

    Department of Economics Vanderbilt University VU Station B#35189 2301 Vanderbilt Place Nashville TN 37215-1819 USA;

    Department of Economics Finance and Quantitative Analysis Kennesaw State University 1000 Chastain Road P.O. Box 0403 Kennesaw GA 30144 USA;

    Department of Economics Vanderbilt University VU Station B#35189 2301 Vanderbilt Place Nashville TN 37215-1819 USA;

    Department of Economics Vanderbilt University VU Station B#35189 2301 Vanderbilt Place Nashville TN 37215-1819 USA;

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