Singular Continuation: Generating Piece-wise Linear Approximations to Pareto Sets via Global Analysis

We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of the Pareto sets, approximating Pareto optima by means of simplicial complexes. The method distinguishes the hierarchy between singular set, Pareto critical set and stable Pareto critical set, and can handle the problem of superposition of local Pareto fronts, occurring in the general nonconvex case. Furthermore, a quadratic convergence result in a suitable set-wise sense is proven and tested in a number of numerical examples.Comment: 29 pages, 12 figure

Individually-rational collective choice

There is a collection of exogenously given socially-feasible sets, and, for each one of them, each individual in a group chooses from an individually-feasible set. The fact that the product of the individually-feasible sets is larger than the socially-feasible set notwithstanding, there arises no conflict between individual choices. Assuming that individual preferences are random, I characterize rationalizable collective choices

Subjective Expected Utility with Non-Increasing Risk Aversion

It is shown that assumptions about risk aversion, usually studied under the pre-supposition of expected utility maximization, have a surprising extra merit at an earlier stage of the measurement work: together with the sure-thing principle, these assumptions imply subjective expected utility maximization for monotonic continuous weak orders

Complementary Patents and Market Structure

Many high technology goods are based on standards that require several essential patents owned by different IP holders. This gives rise to a complements and a double mark-up problem. We compare the welfare effects of two different business strategies dealing with these problems. Vertical integration of an IP holder and a downstream producer solves the double mark-up problem between these firms. Nevertheless, it may raise royalty rates and reduce output as compared to non-integration. Horizontal integration of IP holders solves the complements problem but not the double mark-up problem. Vertical integration discourages entry and reduces innovation incentives, while horizontal integration always benefits from entry and innovatio

On ordinal utility, cardinal utility, and random utility

Though the Random Utility Model (RUM) was conceived  entirely in terms of ordinal utility, the apparatus throughwhich it is widely practised exhibits properties of  cardinal utility.  The adoption of cardinal utility as a  working operation of ordinal is perfectly valid, provided  interpretations drawn from that operation remain faithful  to ordinal utility.  The paper considers whether the latterrequirement holds true for several measurements commonly  derived from RUM.  In particular it is found that  measurements of consumer surplus change may depart from  ordinal utility, and exploit the cardinality inherent in  the practical apparatus.

WARNING: Physics Envy May Be Hazardous To Your Wealth!

The quantitative aspirations of economists and financial analysts have for many years been based on the belief that it should be possible to build models of economic systems - and financial markets in particular - that are as predictive as those in physics. While this perspective has led to a number of important breakthroughs in economics, "physics envy" has also created a false sense of mathematical precision in some cases. We speculate on the origins of physics envy, and then describe an alternate perspective of economic behavior based on a new taxonomy of uncertainty. We illustrate the relevance of this taxonomy with two concrete examples: the classical harmonic oscillator with some new twists that make physics look more like economics, and a quantitative equity market-neutral strategy. We conclude by offering a new interpretation of tail events, proposing an "uncertainty checklist" with which our taxonomy can be implemented, and considering the role that quants played in the current financial crisis.Comment: v3 adds 2 reference

Characterising competitive equilibrium in terms of opportunity

This paper analyses alternative profiles of opportunity sets for individuals in an exchange economy, without assuming that individuals’ choices reveal coherent preferences. It introduces the concept of a ‘market-clearing single-price regime’, representing a profile of opportunity sets consistent with competitive equilibrium. It also proposes an opportunity-based normative criterion, the Strong Opportunity Criterion, which is analogous with the core in preference-based analysis. It shows that every market-clearing single-price regime satisfies the Strong Opportunity Criterion and that, in the limit as an economy is replicated, only such regimes have this property