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

Walter Briec (), Marc Dubois () and Stéphane Mussard ()
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Walter Briec: Lamps, IAE, Université de Perpignan Via Domitia
Marc Dubois: Chrome and Université de Mayotte
Stéphane Mussard: Mohammed VI Polytechnic University

Theory and Decision, 2025, vol. 98, issue 4, No 2, 489-518

Abstract: Abstract 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.

Keywords: Efficiency-inequality trade-off; Inequality aversion; Shapley value; TU-games (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11238-024-10019-7

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