Abstract The purpose of this note is to provide a topological characterization for the existence generalized stable set introduced by Van Deemen (Soc Choice Welf 8:255–260, 1991) as generalization Von Neumann–Morgenstern set.

It is shown that the core of a non-atomic glove-market game which is defined as the minimum of finitely many non-atomic probability measures is a von Neumann Morgenstern stable set. This result is used to characterize some stable sets of large games which have a decreasing returns to scale property. We also study exact non-atomic glove-market games. In particular we show that in a glove-market ...

In the paradigm of von Neumann and Morgenstern, a representation of a ne preferences in terms of an expected utility can be obtained under the assumption of weak continuity. Since the weak topology is coarse, this requirement is a priori far from being negligible. In this work, we replace the assumption of weak continuity by monotonicity. More precisely, on the space of lotteries on a real open...

Players in a game are said to coordinate their behavior if they jointly choose strategies. (The idea goes back to von Neumann [19, 1928] and von Neumann-Morgenstern [21, 1944].) Correlation in behavior arises if players choose their strategies independently, but the choices are conditioned on observations of correlated signals (Aumann [1, 1974]). This note establishes an impossibility result: U...

Nash originated general non-cooperative game theory in seminal articles in the early 1950s by formally distinguishing between non-cooperative and cooperative models and by developing the concept of equilibrium for noncooperative games. Nash developed the first bargaining solution characterized by axioms, pioneered methods and criteria for relating cooperativetheory solution concepts and non-coo...

We establish a link between von Neumann–Morgenstern stable set and the Nash solution in a general n-player utility set. The stable set-solution is defined with respect to a dominance relation: payoff vector u dominates v if one player prefers u even with one period delay. We show that a stable set exists and, if the utility set has a smooth surface, any stable set converges to the Nash bargaini...

5 Bourbaki, N., Elments de Mathematique, Premiere partie, Livre III, Chap. IV, §4, Hermann, Paris, 1942. 6 Eilenberg, S., and Montgomery, D., "Fixed Point Theorems for Multi-valued Transformations," Am. J. Math., 68, 214-222 (1946). 7 Kakutani, S., "A Generalization of Brouwer's Fixed Point Theorem," Duke Math. J., 8, No. 3, 457-459 (September, 1941). 8 Nash, John F., "Equilibrium Points in N-P...