The existence of von Neumann–Morgenstern solutions (stable sets) for assignment games has been an unsolved question since Shapley and Shubik [11]. For each optimal matching between buyers and sellers, Shubik [12] proposed considering the union of the core of the game and the core of the subgames that are compatible with this matching. We prove in the present paper that this set is the unique st...

The following properties of the core of a one-to-one matching problem are well-known: (i) the core is non-empty; (ii) the core is a lattice; and (iii) the set of unmatched agents is identical for any two matchings belonging to the core. The literature on two-sided matching focuses almost exclusively on the core and studies extensively its properties. Our main result is the following characteriz...

the aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von neumann algebra on a hilbert space with a normal faithful semi-finite trace $tau$. the submajorization inequalities generalize some results due to zhang, furuichi and lin, etc..

In this paper, we theoretically characterize robust empirically implementable normative criteria for evaluating socially risky situations. Socially risky situations are modeled as distributions, among individuals, of lotteries on a finite set of statecontingent pecuniary consequences. Individuals are assumed to have selfish Von Neumann-Morgenstern preferences for these socially risky situations...

Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some sufficient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper significantly generalize and improve many known results in...

Solymosi and Raghavan (2001) characterize the stability of the core of the assignment game by means of a property of the valuation matrix. They show that the core of an assignment game is a von Neumann-Morgenstern stable set if and only if its valuation matrix has a dominant diagonal. Their proof makes use of some graphtheoretical tools, while the present proof relies on the notion of buyer-sel...

This paper studies farsighted behavior of firms in an oligopolistic market to form a dominant cartel, which has a power to set and control the price in the market. The von Neumann-Morgenstern stable set is adopted as the solution concept. In contrast to the literature, we do not assume a priori the optimal pricing behavior of the cartel; rather, we show that such behavior arises from the result...