We show that on the domain of convex games, Dutta-Ray's egalitarian solution is characterized by core selection, aggregate monotonicity, and bounded richness, a new property requiring that the poorest players cannot be made richer within the core. Replacing “poorest” by “poorer” allows to eliminate aggregate monotonicity. Moreover, we show that the egalitarian solution is characterized by constrained welfare egalitarianism and either bilateral consistency à la Davis and Maschler or, together with individual rationality, by bilateral consistency à la Hart and Mas-Colell.
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We are grateful to E. Sánchez-Rodríguez for making her joint preprint of the paper Mirás-Calvo et al. (2021) accessible to us and thank two anonymous referees of this journal for their helpful comments and suggestions. The first two authors acknowledge support from research grants ECO2017-86481-P ( AEI/FEDER , UE) and PID2019-105982GB-I00/AEI/10.13039/501100011033 ( MINECO 2019, Spain ), the second author also acknowledges support from Universitat Rovira i Virgili and Generalitat de Catalunya, Spain under projects 2019PFR-URV-B2-53 and 2017SGR770 , and the third author acknowledges support from research grant PID2019-105291GB-I00 ( MINECO 2019, Spain ).
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