Three alternative characterizations of the proportional solution defined on compact and comprehensive bargaining problems with claims are provided. Two new contraction-type and expansion-type axioms are used. Moreover, the single-valuedness axiom is dispensable if the classical symmetry axiom is...

The paper fully characterizes the class of Nash implementable social choice correspondences (SCCs) by mechanisms endowed with Saijo’s message space specification—<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$s$$</EquationSource> </InlineEquation>-mechanisms. This class of SCCs is equivalent to the class of Nash implementable SCCs, though any game form involving...</equationsource></inlineequation>

Benoît and Ok (Games Econ Behav 64:51–67, <CitationRef CitationID="CR1">2008</CitationRef>) show that in a society with at least three agents any weakly unanimous social choice correspondence (SCC) is Maskin’s monotonic if and only if it is Nash-implementable via a simple stochastic mechanism (Benoît-Ok’s Theorem). This paper...</citationref>

A choice correspondence is weak justified if a non-chosen alternative is dominated by any other obtainable alternative, and for each discarded alternative there is some chosen alternative which dominates it. This definition allows us to build a connection between the behavioral property...