The notion of ‘mathematical impossibility’ of group decision making is founded on errors in microeconomics, game theory, and related disciplines. We highlight mathematical errors that have been committed by von Neumann and Morgenstern, Pareto, Hicks, Samuelson, and Debreu which have been propagated throughout the social sciences. Applicability of Mathematical Operations

This article presents a generalization of the equilibrium analysis for the simple two-player poker game with alternate bidding of Von Neumann and Morgenstern. It approximates optimal play for this game if it is played with a regular deck of 52 cards and it discusses some strategic insights. In addition, the paper studies the relative skill level of this game.

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

The concept of stability á la J. von Neumann and O. Morgenstern, which is composed of a pair of internal and external stability requirements, formalizes the idea of standard of behavior. This paper studies the decisiontheoretic foundation of stability, by establishing some epistemic conditions for a “stable” pattern of behavior in the context of strategic interaction. JEL Classification: C70, C...

Qualitative counterparts of expected utility can be expressed by means of Sugeno inte-grals. Both von Neumann and Morgenstern-like and Savage-like axiomatic justiications are provided. In this framework, pessimistic (i.e., risk-averse) as well as optimistic attitudes can be captured.

In this paper we show that every finite-player game in characteristic function form obeying an innocuous condition (that the set of individually rational pay-off vectors are bounded) possesses a farsighted von-Neumann-Morgenstern stable set. JEL Classification No.: C71, D71.

Existence of von Neumann–Morgenstern solutions (stable sets) is proved for any assignment game. For each optimal matching, a stable set is defined as the union of the core of the game and the core of the subgames that are compatible with this matching. All these stable sets exclude third-party payments and form a lattice with respect to the same partial order usually defined on the core.

Westudy abstract decision problems by introducing an extended dominance relation with respect to a set of alternatives. This extension is in between the traditional dominance relation as formulated by Von Neumann and Morgenstern (Theory of games and economic behavior, Princeton University Press, Princeton, 1944) and the transitive closure of it. Subsequently, stable sets are defined and studied...

In Possibilistic Decision Theory (PDT), decisions are ranked by a pessimistic and an optimistic qualitative criteria. The preference relations induced by these criteria have been axiomatized by corresponding sets of rationality postulates, both à la Neumann-Morgenstern and à la Savage. In this paper we first address a particular issue regarding the axiomatic systems of PDT à la von Neumann and ...

ing interaction among rational and self-interested agents. The field took on its modern form in the 1940s and 1950s (von Neumann and Morgenstern 1947; Nash 1950, Kuhn 1953), with even earlier antecedents (such as Zermelo 1913 and von Neumann 1928). Although it has had occasional and significant overlap with computer science over the years, game theory received most of its early study by economi...