This paper takes the Anscombe-Aumann framework with horse and roulette lotteries, and applies the Savage axioms to the horse lotteries and the von Neumann-Morgenstern independence axiom to the roulette lotteries. The resulting representation of preferences yields a subjective probability measure over states and two utility functions, one governing risk attitudes and one governing ambiguity atti...

We apply the von Neumann-Morgenstern stable set to the n-player cake division problem. Only time-preferences á la Rubinstein (1982) are assumed. The stable set is defined with respect to the following dominance relation: x dominates y if there is a player who prefers x over y even with one period lag. The Nash bargaining solution is characterized in the language of stable sets. Through the char...

In this paper we propose a new method to associate a coalitional game with each strategic game. The method is based on the lower value of matrix games. We axiomatically characterize this new method, as well as the method that was described in von Neumann and Morgenstern (1944). As an intermediate step, we provide some axiomatic characterizations of the value and the lower value of matrix games.

This overview focuses on lexicographic choice under conditions of uncertainty. First, lexicographic versions of traditional (von Neumann-Morgenstern) expected utility theory are described where the usual Archimedean axiom is weakened. The role of these lexicographic variants in explaining some well-known “paradoxes” of choice theory is reviewed. Next, the significance of lexicographic choice fo...

This note investigates the noncooperative foundations of von Neumann-Morgenstern (vN-M) stable sets in voting games. To do so, we study subgame perfect equilibria of a noncooperative legislative bargaining game, based on underlying simple games. The following results emerge from such an exercise: Every stable set of the underlying simple game is the limit set of undominated pure-strategy Markov...

The Fudenberg and Maskin folk theorem for discounted repeated games assumes that the set of feasible payoffs is full dimensional . We obtain the same conclusion using a weaker condition. This condition is that no pair of players has equivalent von Neumann-Morgenstern utilities over outcomes. We term this condition NEU ("non-equivalent utilities"). The condition is weak, easily interpreted, and ...

We consider the allotment problem of homogeneous indivisible goods among agents with single-peaked and risk-averse von Neumann-Morgenstern expected utility functions. We establish that a rule satisfies coalitional strategy-proofness, same-sideness, and strong symmetry if and only if it is the uniform probabilistic rule. By constructing an example, we show that if same-sideness is replaced by re...

We establish a general n-player link between non-cooperative bargaining and the Nash solution. Non-cooperative bargaining is captured in a reduced form through the von Neumann-Morgenstern (1944) stability concept. A stable set always exists. Moreover, if the utility set has a smooth surface, then any stable set converges to the Nash bargaining solution. Finally, the equivalence of stationary eq...

What value should we put on chances? This paper examines the hypothesis that, contra the widely accepted theory of von Neumann and Morgenstern, chances can have diminishing marginal value. The hypothesis is defended by showing that it can be used to explain both the typical pattern of preferences observed in the Ellsberg paradox and the intuition that lotteries are the best way to distribute in...

The paper introduces a new notion of risk aversion that is independent of the good under observation and its measure scale. The representational framework builds on a time consistent combination of additive separability on certain consumption paths and the von Neumann & Morgenstern (1944) assumptions. In the one-commodity special case, the new notion of risk aversion closely relates to a disent...