We examine here the quasi-transitivity axiom which is considered to be a minimal criterion which a rational preference should respect. We check for the consistency of this axiom with the well-known theory if choice function.

This survey paper prepared for the Handbook of Utility Theory covers the axiomatic foundation of decision making under uncertainty when conditional preferences are allowed to be state dependent, leading to an expected state-dependent utility representation.

The paper argues for the formal investigation of conditions under which that preference reltions are definable in various simple languages. An example of such an investigation is given.

Bergin and Lipman (1996) show that the refinement effect from the random mutations in the adaptive population dynamics in Kandori, Mailath and Rob (1993) and Young (1993) is due to restrictions on how these mutation rates vary across population states. We here model mutation rates as...

Bergin and Lipman (1996) show that the refinement effect from the random mutations in the adaptive population dynamics in Kandori, Mailath and Rob (1993) and Young (1993) is due to restrictions on how these mutation rates vary across population states. We here model mutation rates as...

We build spaces of q.p. (quasi-periodic) functions and we establich some of their properties. They are motivated by the Perceival approach to q.p. solutions of Hamiltonian systems. The periodic solutions of an adequat Partial Differential Equation are related to the q.p. solutions of an Ordinar...

In the first part of this paper we prove that the global quadratic optimization problem over a simplex can be solved with a constant relative accuracy. In the second part we consider some natural extensions of the result.

This paper presents a combinatorial polynomial-time algorithm for minimizing submodular set functions. The algorithm employs a scaling scheme that uses a flow in the complete directed graph on the underlying set with each arc capacity equal to the scaled parameter.

Evidence such as the Ellsberg Paradox shows that decision-makers do not assign probabilities to all events. It is intuitive that they may differ not only in the probabilities assigned to given events but also in the identity of the events to which they assign probabilities. This paper describes...

Five decades ago, Bhattacharyya established a series of lower bounds for the variance of an unbiased estimator, since then called the Bhattacharyya bounds. In 1974 Blight and Rao have shown that the series of Bhattacharyya bounds converges to the variance of the best unbiased estimator. In this...