Heterogeneity in Economics

This paper argues that heterogeneity of agents’ characteristics plays a fundamental role in the economy and should do so in economic models. Three aspects are considered. Firstly the notion that assuming heterogeneity was a solution to the problem posed by the results of Sonnenschein Mantel and Debreu is considered and it is suggested that the more pragmatic approach adopted by Hildenbrand is likely to be more productive. Next the role of adaptation and evolution which necessarily involve variety or heterogeneity is examined. It is suggested that heterogeneity will persist since agents will only slowly learn to adapt and that in the meantime the environment will change. Lastly the role of heterogeneity in financial markets is examined. It is suggested that heterogeneous and varying expectations may account for many of the stylised facts which do not seem to be consistent with the standard financial markets model.“Variety is the spice of life”     

The impossibility of compromise: some uniqueness properties of expected utility preferences

Summary. We focus on the following uniqueness property of expected utility preferences: Agreement of two preferences on one interior indifference class implies their equality. We show that, besides expected utility preferences under (objective) risk, this uniqueness property holds for subjective expected utility preferences in Anscombe-Aumann's (partially subjective) and Savage's (fully subjective) settings, while it does not hold for subjective expected utility preferences in settings without rich state spaces. Indeed, when it holds the uniqueness property is even stronger than described above, as it needs only agreement on binary acts. The extension of the uniqueness property to the subjective case is possible because beliefs in the mentioned settings are shown to satisfy an analogous property: If two decision makers agree on a likelihood indifference class, they must have identical beliefs. Received: November 15, 1999; revised version: December 29, 1999     

Testing for a unique equilibrium in applied general equilibrium models

This paper introduces a new and computationally inexpensive method to test for uniqueness of equilibrium in exchange economies.     

Is algorithm aversion WEIRD? A cross-country comparison of individual-differences and algorithm aversion

Although algorithms offer superior performance over humans across many tasks, individuals often exhibit algorithm aversion, resisting algorithmic advice in favour of human recommendations. However, most algorithm aversion studies rely on American samples, potentially limiting the generalisability of the findings. Given the increasing adoption of algorithms globally, we explore if the impact of two crucial factors driving algorithm aversion, uniqueness neglect and familiarity, differ between culturally different countries. Drawing on the individualism-collectivism cultural dimension, we conducted two online studies comparing algorithm aversion between people in India and the United States in medical and financial services scenarios. While our results suggest that there is no difference in the degree of algorithm aversion between Indians and Americans at an aggregate level, we find important cross-cultural differences: Uniqueness neglect strengthens algorithm aversion for Americans more than Indians, while familiarity weakens algorithm aversion more for Indians than Americans. Thus, our results reveal generalisability issues within the algorithm aversion literature, as factors influencing algorithm aversion can be culturally dependent.     

The Color of Choice: The Influence of Presenting Product Information in Color on the Compromise Effect

Consumers often find themselves challenged by the conflicting desires to seek uniqueness versus conformity, and thus seek some degree of balance. In a series of six studies we show that presenting each options’ product-related information in a unique color, as opposed to all product-related information presented in black-on-white, partially satiates the desire for uniqueness, thus amplifying the compromise effect. Consumers facing color presentation formats choose the middle, conforming option more often, yet perceive their choice as more unique. This color effect is not realized if each option's attributes are presented in different colors, but all options use a consistent color scheme, as is often the case in on-line retailing sites such as Amazon.com. Having to justify one's choice moderates the color effect. The practical take-away is that consumers’ choices can be influenced by using unique colors to present option-related product information, a variable that is entirely independent of the options’ performance characteristics. Two field studies confirm this finding, one using a plain background versus a colored background in a product display and the other using product containers that are either in plain white or wrapped in unique colors.     

The number of equilibria of smooth infinite economies

We construct an index theorem for smooth infinite economies that shows that generically the number of equilibria is odd. As a corollary, this gives a new proof of existence and gives conditions that guarantee global uniqueness of equilibria.     

All equilibria of the multi-unit Vickrey auction

This paper completely characterizes the set of equilibria of the Vickrey auction for multiple identical units when buyers have non-increasing marginal valuations and there are at least three potential buyers. There are two types of equilibria: In the first class of equilibria there are positive bids below the maximum valuation. In this class, above a threshold value all bidders bid truthfully on all units. One of the bidders bids at the threshold for any unit for which his valuation is below the threshold; the other bidders bid zero in this range. In the second class of equilibria there are as many bids at or above the maximum valuation as there are units. The allocation of these bids is arbitrary across bidders. All the remaining bids equal zero. With any positive reserve price equilibrium becomes unique: Bidders bid truthfully on all units for which their valuation exceeds the reserve price.     

Regularity and robustness in monotone Bayesian games

This paper defines regular and weakly regular equilibria for monotone Bayesian games with one-dimensional actions and types. It analyzes the robustness of equilibria with respect to perturbations. It also proves an index theorem and provides applications to uniqueness of equilibrium.     

Existence,uniqueness, and stability of equilibrium in an OLG economy

Summary. This paper presents sufficient conditions for the existence of a unique and globally stable steady state equilibrium for OLG economies with production. The conditions impose separate requirements on the utility and production functions. Moreover, the conditions do not require assumptions concerning the third order derivatives of the production and utility functions.Received: 12 August 2002, Revised: 7 January 2003, JEL Classification Numbers: D50, D91, E13, O41.I would like to thank Nick Baigent, Laurie Conway, Karl Farmer, Christian Gehrke, and Hideo Konishi for helpful comments. I am grateful to an anonymous referee for his or her comments.     

Multiple solutions under quasi-exponential discounting

Infinite horizon dynamic optimization problems with non-exponential time preferences may not only exhibit time inconsistency but may also have multiple solutions with distinct payoffs. We here show that such multiplicity is generic in the sense that it occurs in an open set of such decision problems, even with small state- and action-spaces. Non-exponential discounting allows for an “addictive” equilibrium alongside a “virtuous” equilibrium. We also provide a sufficient condition for uniqueness in infinitely repeated decision problems with general action spaces. Authors thank Philippe Jehiel, Maria Saez-Marti and Bill Sandholm for comments to an earlier version, and the Knut and Alice Wallenberg Research Foundation for financial support.