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Cost of Inequality, the Uniform Rule and Cooperative Games


  • Arsen Palestini

    () (MEMOTEF, Sapienza University of Rome, Via del Castro Laurenziano 9, 00161 Rome, Italy.)

  • Giuseppe Pignataro

    () (Department of Economics, University of Bologna, Strada Maggiore 45, 40125 Bologna, Italy.)


The assessment of income inequality can be investigated looking at the solution concepts of the cooperative game theory. We propose a multi-factorial decomposition of the Atkinson index by income sources and evaluate it as a cooperative game of the social cost of inequality. This framework extends the distributive and efficient properties of the uniform rule (Sprumont [35]) in a setup with heterogeneous income sources and single-peaked preferences. We provide an axiomatic foundation of this preference-based allocation rule, called weakly uniform rule, with a further comparison with the solution concept of nucleolus. Sufficient conditions for their coincidence are therefore defined. Finally we characterize a welfare loss game expressed as the difference between the sum of inequalities generated by each source and the cost of the entire distribution. We show that income factors' contributions may increase or decrease the income inequality in the society ensuring different perspectives in terms of public policies.

Suggested Citation

  • Arsen Palestini & Giuseppe Pignataro, 2014. "Cost of Inequality, the Uniform Rule and Cooperative Games," Working Papers 322, ECINEQ, Society for the Study of Economic Inequality.
  • Handle: RePEc:inq:inqwps:ecineq2014-322

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    Atkinson index; cost game; uniform rule; income sources; single-peaked preferences.;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D33 - Microeconomics - - Distribution - - - Factor Income Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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