To allow conditioning on counterfactual events, zero probabilities can be replaced by infinitesimal probabilities that range over a non-Archimedean ordered field. This paper considers a suitable minimal field that is a complete metric space. Axioms similar to those in Anscombe and Aumann (1963) and in Blume, Brandenburger and Dekel (1991) are used to characterize preferences which: (i) reveal u...

In this paper we study a Markov decision process with a non-linear discount function. Our approach is in spirit of the von Neumann-Morgenstern concept and is based on the notion of expectation. First, we define a utility on the space of trajectories of the process in the finite and infinite time horizon and then take their expected values. It turns out that the associated optimization problem l...

This paper extends the expected utility models of decision making under risk and under uncertainty to include incomplete beliefs and tastes. The main results are two axiomatizations of the multiprior expected multi-utility representations of preference relation under uncertainty, thereby resolving long standing open questions. The Knightian uncertainty model and expected multi-utility model wit...

We characterize when choices among lotteries over arbitrary allocations are monotonic in an expected-utility agent’s type. Our necessary and sufficient condition is on the von Neumann-Morgenstern utility function; we identify an order over lotteries that generates the choice monotonicity when the condition holds. We discuss applications to cheap-talk games, costly signaling games, and collectiv...

The comparative statics of the optimal portfolios across individuals is carried out for a continuous-time complete market model, where the risky assets price process follows a joint geometric Brownian motion with time-dependent and deterministic coefficients. It turns out that the indirect utility functions inherit the order of risk aversion (in the Arrow-Pratt sense) from the von Neumann-Morge...

Classical foundations of expected utility were provided by Ramsey, de Finetti, von Neumann and Morgenstern, Anscombe and Aumann, and others. These foundations describe preference conditions to capture the empirical content of expected utility. The assumed preference conditions, however, vary among the models and a unifying idea is not readily transparent. Providing such a unifying idea is the p...

Because players whose preferences violate the von Neumann-Morgenstern independence axiom may be unwilling to randomize as mixed-strategy Nash equilibrium would require, a Nash equilibrium may not exist without independence. This paper generalizes Nash’s definition of equilibrium, retaining its rationalexpectations spirit but relaxing its requirement that a player must bear as much uncertainty a...

We present the first polynomial-time algorithm for computing the minimal covering set of a (weak) tournament. The algorithm is based on a linear programming formulation of a subset of the minimal covering set known as the essential set. On the other hand, we show that no efficient algorithm exists for two variants of the minimal covering set, the minimal upward covering set and the minimal down...

The stable set of von Neumann and Morgenstern imposes credibility on coalitional deviations. Their credibility notion can be extended to cover farsighted coalitional deviations, as proposed by Harsanyi (1974), and more recently reformulated by Ray and Vohra (2015). However, the resulting farsighted stable set suffers from a conceptual drawback: while coalitional deviations improve on existing o...

Keynes and Knight make a clear distinction between two kinds of uncertainty : the first one, called risk, may be characterized by probabilities, while this is not possible for the second one. Here we deal with decision-making under genuine uncertainty, no probability distributions being available. We first consider criteria to accept some piece of information as reliable. And we examine the pos...