We analyze decision-makers who make stochastic choices from sets of lotteries. A random choice rule associates with each decision problem a probability measure over the feasible choices. A random utility is a probability measure over von Neumann-Morgenstern utility functions. We show that a random choice rule maximizes some random utility if and only if it is mixture continuous, monotone (the p...

We show that the core of a continuous convex game on a measurable space of players is a von Neumann Morgenstern stable set. We also extend the definition of the Mas Colell bargaining set to games with a measurable space of players and show that for continuous convex games the core may be strictly included in the bargaining set but it coincides with the set of all countably additive payoff measu...

This paper axiomatizes expected multi-utility representations of incomplete preferences under risk and under uncertainty. The von Neumann–Morgenstern expected utility model with incomplete preferences is revisited using a ‘‘constructive’’ approach, as opposed to earlier treatments that use convex analysis. © 2012 Elsevier B.V. All rights reserved. ‘‘Of all the axioms of utility theory, the comp...

I generalize the Von Neumann-Morgenstern (vNM) Expected Utility Theorem in the case of a finite set by weakening the Independence and Continuity axioms. In the resulting representation a lottery ∑ πixi is evaluated by ∑ Ψ(πiu(xi)), where the shape of Ψ determines what I call mixture attitudes. I consider three extensions: 1) allowing mixture-seeking attitudes in addition to mixture-averse attit...

There are n agents who have von Neumann-Morgenstern utility functions on a finite set of alternatives A. Each agent i’s utility function is known to lie in the nonempty, convex, relatively open set Ui. Suppose L is a lottery on A that is undominated, meaning that there is no other lottery that is guaranteed to Pareto dominate L no matter what the true utility functions are. Then, there exist ut...

We introduce a procedural model of risky choice in which an individual is endowed with a core preference relation that may be highly incomplete. She can, however, derive further rankings of alternatives from her core preferences by means of a procedure based on the independence axiom. We find that the preferences that are generated from an initial set of rankings according to this procedure can...

The paper discusses criteria for comparing risk aversion of decision makers when outcomes are multidimensional. A weak concept, ”commodity specific greater risk aversion”, is based on the comparison of risk premia paid in a specified commodity. A stronger concept, ”uniformly greater risk aversion” is based on the comparison of risk premia regardless of what commodities are used for payment. Nei...

We prove the existence of general equilibrium for continuous-time overlappinggenerations models. Previous theorems exclude all non-linear C.E.S. and von Neumann Morgenstern preferences and exclude production. Our primitive assumptions are satisfied by such preferences and by all Markovian production technologies satisfying Bewley's assumptions for Arrow Debreu models provided that storage is po...

The von Neumann-Morgenstern concept of solution is applied to nonatomic pure exchange markets consisting of a finite number of different types of trader, initially owning disjoint sets of goods. It is proved that if all traders of each type form a cartel and behave like a single (atomic) trader (their "representative"), then one gets solutions of the original market from those of the finite mar...

This paper presents a new approach to decision-making under risk. Preference over risky prospects is defined as a triadic reference-dependent relation in a sense similar to Sugden (2003). Characterized by a set of von Neumann-Morgenstern-style axioms, a new reference-dependent representation theory – called compound utility theory (CUT) – is obtained which accommodates nonlinear preferences (in...