We suggest a concept of convexity of preferences that does not rely on any algebraic structure. A decision maker has in mind a set of orderings interpreted as evaluation criteria. A preference relation is defined to be convex when it satisfies the following: if for each criterion there is an...

A discrete symmetry of a preference relation is a mapping from the domain of choice to itself under which preference comparisons are invariant; a continuous symmetry is a one-parameter family of such transformations that includes the identity; and a symmetry field is a vector field whose...

Even the most rudimentary training from Economics 101 starts with demand curves going down and supply curves going up. They are so 'natural' that they sound even more obvious than the Euclidian postulates in mathematics. But are they? What do they actually mean? Start with "demand curves". Are...

Boards hire and fire CEOs based on imperfect information. Using comprehensive data on 28 cohorts in Sweden, we analyze the role of a potentially important unobserved attribute - CEO health - in corporate governance. We find CEOs are significantly healthier than the population and other highskill...

Artificial Intelligence (AI) scientists are challenged to create intelligent, autonomous agents that can make rational decisions. In this challenge, they confront two questions: what decision theory to follow and how to implement it in AI systems. This paper provides answers to these questions...

We provide characterizations of preferences representable by a Cobb-Douglas utility function.

In most economics textbooks there is a gap between the non-existence of utility functions and the existence of continuous utility functions, although upper semi-continuity is sufficient for many purposes. Starting from a simple constructive approach for countable domains and combining this with...

We develop a sequential trade model of Iceberg order execution in a limit order book. The Iceberg-trader has the freedom to expose his trading intentions or (partially) shield the true order size against other market participants. Order exposure can cause drastic market reactions ('market...

Since Paul Samuelson introduced the theory of revealed preference, it has become one of the most important concepts in economics. This chapter surveys some recent contributions in the revealed preference literature. We depart from Afriat's theorem, which provides the conditions for a data set to...