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 considers an exchange economy under uncertainty with asymmetric information. Uncertainty is represented by multiple priors and posteriors of agents who have either Bewley's incomplete preferences or Gilboa-Schmeidler's maximin expected utility preferences. The main results...

Recently, various types of Social Networking Service (SNS) have been actively utilized in many educational situations, and the effectiveness has been continuously reported. The aim of this paper is to develop a web based discussion support system, to introduce the proposed system to a real...

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>

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>