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...

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>

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 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...