Continuous lexicographic preferences

Under what conditions are lexicographically representable preferences continuously representable? This question is actually two questions, since there are two natural definitions of continuity for lexicographic representations. A complete answer is given for one of these questions, and the other is answered for two dimensional lexicographic representations.     

Continuous mean demand functions derived from non-convex preferences

In this paper we show that for a large subset of utility functions in the space of all C¹ utility functions and for all prices the mean demand of those consumers whose taste is represented by a given utility function in that subset is uniquely determined. This implies that for a large set of economies mean demand is a continuous function. Our analysis uses derivatives of first and of higher order. The result is essentially a consequence of the multijet transversality theorem.     

Continuous representation of Von Neumann–Morgenstern preferences

This paper considers a continuous representation of preference relations satisfying Grandmont's (1972) Expected Utility Hypothesis. We equip the preferences with the topology of closed convergence, then we show the existence of a jointly continuous expected utility function and consider its uniqueness. Furthermore, we construct an embedding map of the preferences into the set of expected utility functions.     

Endowment-regarding preferences

We consider a general equilibrium model of pure exchange economies with endowment externalities. Consumers’ behaviors depend not only on their own consumption but also on the endowments of the other consumers. Applying the same method of analysis in Balasko (2015) about wealth concerns, we first show that almost all properties of equilibrium, including smooth equilibrium manifold and genericity of regular economies, can be directly extended to the economy where the demand function depends on the endowments of others and wealth of only one consumer. Next, we clarify the sufficient conditions under which those properties remain true in the economy with the most general form of endowment externalities. Finally, we generalize the above sufficient conditions to derive generic regularity results in the economy with both consumption and endowment externalities.     

Euclidean preferences

This note is devoted to the question: how restrictive is the assumption that preferences be Euclidean in d dimensions. In particular it is proven that any preference profile with I individuals and A alternatives can be represented by Euclidean utilities with d   dimensions if and only if d≥min?(I,A−1)$d\ge \min ?(I\text{,}A-1)$. The paper also describes the systems of A points which allow for the representation of any profile over A alternatives, and provides similar results when only strict preferences are considered. These findings contrast with the observation that if preferences are only required to be convex then two dimensions are always sufficient.     

Approximation of convex preferences

It is shown geometrically that a monotone concave preference order can be approximated by orders representable by a concave utility function. This is applied to proving that preferences with ‘desirable’ properties (such as inducing smooth excess demand functions, analyticity, strict convexity) are dense.     

Closure and preferences

We investigate the results of Kreps (1979), dropping his completeness axiom. As an added generalization, we work on arbitrary lattices, rather than a lattice of sets. We show that one of the properties of Kreps is intimately tied with representation via a closure operator. That is, a preference satisfies Kreps’ axiom (and a few other mild conditions) if and only if there is a closure operator on the lattice, such that preferences over elements of the lattice coincide with dominance of their closures. We tie the work to recent literature by Richter and Rubinstein (2015).     

Characterizing lexicographic preferences

We characterize lexicographic preferences on product sets of finitely many coordinates. The main new axiom is a robustness property. It roughly requires this: Suppose $x$ is preferred to $y$; many of its coordinates indicate that the former is better and only a few indicate the opposite. Then the decision maker is allowed a change of mind turning one coordinate in favor of $x$ to an indifference: even if one less argument supports the preference, the fact that we started with many arguments in favor of $x$ suggests that such a small change is not enough to give rise to the opposite preference.     

Demand properties of concavifiable preferences

The purpose of the present paper is to clarify the relation between choice theory for individual consumers, i.e., the observed demand behavior, and the preference ordering ?$?$ of that individual. Specifically, we study how concavifiability (i.e., representability of ?$?$ by a concave utility function) is expressed by quantities (cross-coefficients) appearing in revealed preferences theory. We present a sequence of rather explicit necessary conditions for concavifiability. All these conditions are quantitative asymptotic strengthenings of the strong axiom of revealed preference. The results and concepts are illustrated by means of examples in which an expenditure data is defined by providing its generating utility function.     

Quantification of preferences in markets

In this paper we quantify agent preferences in a market. In our framework every agent has a utility level associated with each transaction, and we assume that the probability of a feasible market transaction increases with an increase in total utility. It is surprising to observe that this simple behavioral principle induces a usually unique probability measure that can be constructed by a fast numerical algorithm. This unusual combination of a rigorous model and a fast numerical algorithm makes it possible to construct a well-defined set of preferences that implies a set of observed commodity prices.     

Weighted distances between preferences

Individual disagreements are assumed to be reflected in the preferences. Distance functions, e.g., the well-known Kemeny (1959) metric, are used to measure these disagreements. However, a disagreement on how to rank the top two alternatives may be perceived more (or less) than a disagreement on how to rank the bottom two alternatives. We propose two conditions on functions which characterize a class of weighted semi-metric functions. This class of semi-metrics allows to quantify disagreements according to where they occur in preferences. It turns out one of these functions, “the path minimizing function”, is the only metric which generalizes the Kemeny metric.     

Revising preferences and choices

Preferences and choices are subject to be modified when new information is brought to the knowledge of an agent, such strategy may suddenly appear more reliable than such other, such restaurant has to be retrieved from the list of the ten best tables of the town. We propose here an easy way to perform this revision through a simple modification of the chain of subsets attached to the agent’s behavior: it can be shown indeed that, in the rational case, these chains offer an adequate representation of preferences and of choice functions. Thus the revision problem boils down to adding, retracting or modifying some of the links of the original chain, a perspective that enables an effective treatment of the problem of iterated revision.     

Evolutionary stability of prospect theory preferences

We demonstrate that in simple 2×2 games (cumulative) prospect theory preferences can be (semi-)evolutionarily stable, in particular, a population of players with prospect theory preferences is stable against more rational players, i.e. players with a smaller degree of probability weighting. We also show that in a typical game with infinitely many strategies, the “war of attrition”, probability weighting is (semi-)evolutionarily stable. Finally, we generalize to other notions of stability. Our results may help to explain why probability weighting is generally observed in humans, although it is not optimal in usual decision problems.     

Agricultural arbitrage and risk preferences

A structural intertemporal model of agricultural asset arbitrage equilibrium is developed and applied to agriculture in the North Central region of the US. The data are consistent with a unifying level of risk aversion. The levels of risk aversion are more plausible than previous estimates for agriculture. However, the standard arbitrage equilibrium is rejected; perhaps, this is due to the period and the shortness of the period studied.