The purpose of this paper is twofold. First, we generalize Kajii et al. (J Math Econ 43:218–230, <CitationRef CitationID="CR16">2007</CitationRef>) and provide a condition under which for a game <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$v$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>v</mi> </math> </EquationSource> </InlineEquation>, its Möbius inverse is equal to zero within the framework of the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$k$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>k</mi> </math> </EquationSource> </InlineEquation>-modularity of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$v$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>v</mi> </math> </EquationSource> </InlineEquation> for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$k \ge 2$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>k</mi>...</mo></mrow></math></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></citationref>

The purpose of this paper is twofold. First, we generalize Kajii et al. (2007), and provide a condition under which for a game v, its Mobius inversion is equal to zero within the framework of the k-modularity of v for k = 2. This condition is more general than that in Kajii et al. (2007)....

This paper proposes a class of independence axioms for simple acts. By introducing the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathcal {E}}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="script">E</mi> </math> </EquationSource> </InlineEquation>-cominimum independence axiom that is stronger than the comonotonic independence axiom but weaker than the independence axiom, we provide a new axiomatization theorem of simple acts...</equationsource></equationsource></inlineequation>

This paper proposes a class of independence axioms for simple acts. By introducing the E-cominimum independence axiom that is stronger than the comonotonic independence axiom but weaker than the independence axiom, we provide a new axiomatization theorem of simple acts within the framework of...

In order to describe partial cooperation structures, this paper introduces complete coalition structures as sets of feasible coalitions. A complete coalition structure has a property that, for any coalition, if each pair of players in the coalition belongs to some feasible coalition contained in...

In order to describe partial cooperation structures, this paper introduces complete coalition structures as sets of feasible coalitions. A complete coalition structure has a property that, for any coalition, if each pair of players in the coalition belongs to some feasible coalition contained in...

This paper proposes a class of weak additivity concepts for an operator on the set of real valued functions on a finite state space Ω, which include additivity and comonotonic additivity as extreme cases. Let E ⊆ 2Ω be a collection of subsets of Ω. Two functions x and y on Ω are...

This paper proposes a class of weak additivity concepts for an operator on the set of real valued functions on a finite state space \omega, which include additivity and comonotonic additivity as extreme cases. Let \epsilon be a collection of subsets of \omega. Two functions x and y on \omega are...

In this paper, we consider the problem of ranking linear budget sets with different available goods. We introduce axioms that are based on preference-based and preference-independent views of evaluating freedom, as well as two basic axioms. By using these axioms, we characterize two ranking rules.