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<p>A family of single-parameter Atkinson–Shapley rules for TU-games is introduced. These rules are marginalist with a specific transformation of the marginal contributions depending on a parameter, which assesses how equality among payoffs fairly offsets inefficiency in the redistribution. This normative content is similar in spirit to that of Atkinsonian social welfare functions. It is shown that the higher the value of the parameter (being positive), the greater the social welfare of the resulting distribution of payoffs according to the so-called <i>generalized Lorenz</i> criterion. The Atkinson–Shapley rules are relevant to propose solutions in cases where redistributed payoffs must exceed the worth of the grand coalition. This point is illustrated through an example involving a public pension system with unfunded liabilities.</p>

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Atkinson–Shapley rules for TU-games: on the trade-off between efficiency and inequality

  • 期刊论文

  • 发表日期：

    2025年1月9日

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  • Walter Briec,
  • Marc Dubois,
  • Stéphane Mussard

摘要

A family of single-parameter Atkinson–Shapley rules for TU-games is introduced. These rules are marginalist with a specific transformation of the marginal contributions depending on a parameter, which assesses how equality among payoffs fairly offsets inefficiency in the redistribution. This normative content is similar in spirit to that of Atkinsonian social welfare functions. It is shown that the higher the value of the parameter (being positive), the greater the social welfare of the resulting distribution of payoffs according to the so-called generalized Lorenz criterion. The Atkinson–Shapley rules are relevant to propose solutions in cases where redistributed payoffs must exceed the worth of the grand coalition. This point is illustrated through an example involving a public pension system with unfunded liabilities.