Singleton bias and lexicographic preferences among equally valued alternatives

Two experiments examined a form of singleton bias deducible from lexicographic choice and Tversky’s theory of elimination by aspects. In Experiment 1, 100 decision makers who chose from a set of job applicants defined by equal numbers of equally important qualifications tended to ignore the singleton defined by possession of a relevant attribute but tended to rank-order the attributes as predicted by lexicographic choice theory and showed various forms of singleton bias. In Experiment 2, 100 decision makers who chose from sets of unspecified alternatives, universities, and houses/apartments defined by attributes that they had individually rated as equally important ignored the attribute-defined singleton in every alternative set but manifested a different singleton bias in favor of the middle option of the on-screen display.     

Nash equilibrium in games with incomplete preferences

Summary. This paper investigates Nash equilibrium under the possibility that preferences may be incomplete. I characterize the Nash-equilibrium-set of such a game as the union of the Nash-equilibrium-sets of certain derived games with complete preferences. These games with complete preferences can be derived from the original game by a simple linear procedure, provided that preferences admit a concave vector-representation. These theorems extend some results on finite games by Shapley and Aumann. The applicability of the theoretical results is illustrated with examples from oligopolistic theory, where firms are modelled to aim at maximizing both profits and sales (and thus have multiple objectives). Mixed strategy and trembling hand perfect equilibria are also discussed.Received: 22 September 2003, Revised: 24 June 2004, JEL Classification Numbers: D11, C72, D43.I would like to thank Jean-Pierre Benôit, Juan Dubra, Alejandrio Jofre, Debraj Ray, Kim-Sau Chung and the seminar participants at NYU and at the Universidad de Chile for their comments. I am most grateful to Efe Ok, for his comments, criticism, suggestions and questions.     

Evolutionary dynamics and backward induction

The backward induction (or subgame-perfect) equilibrium of a perfect information game is shown to be the unique evolutionarily stable outcome for dynamic models consisting of selection and mutation, when the mutation rate is low and the populations are large.     

The structure of the Nash equilibrium sets of standard 2-player games

Summary. In this paper I study a class of two-player games, in which both players action sets are [0,1] and their payoff functions are continuous in joint actions and quasi-concave in own actions. I show that a no-improper-crossing condition is both necessary and sufficient for a finite subset A of to be the set of Nash equilibria of such a game.Received: 21 November 2002, Revised: 9 September 2004, JEL Classification Numbers: C65, C72.I am grateful to an editor of the journal and an anonymous referee for their very helpful comments. I also would like to thank the seminar participants at City University of Hong Kong, Georgia State University, Northwestern University, and Rice University.     

Nash equilibrium when players account for the complexity of their forecasts

Nash equilibrium is often interpreted as a steady state in which each player holds the correct expectations about the other players' behavior and acts rationally. This paper investigates the robustness of this interpretation when there are small costs associated with complicated forecasts. The model consists of a two-person strategic game in which each player chooses a finite machine to implement a strategy in an infinitely repeated 2×2 game with discounting. I analyze the model using a solution concept called Nash Equilibrium with Stable Forecasts (ESF). My main results concern the structure of equilibrium machine pairs. They provide necessary and sufficient conditions on the form of equilibrium strategies and plays. In contrast to the “folk theorem,” these structural properties place severe restrictions on the set of equilibrium paths and payoffs. For example, only sequences of the one-shot Nash equilibrium can be generated by any ESF of the repeated game of chicken.     

Cournot–Nash equilibria in continuum games with non-ordered preferences

In the usual framework of continuum games with externalities, we substantially generalize Cournot–Nash existence results [Balder, A unifying approach to existence of Nash equilibria, Int. J.Game Theory 24 (1995) 79–94; On the existence of Cournot–Nash equilibria in continuum games, J. Math. Econ. 32 (1999) 207–223; A unifying pair of Cournot–Nash equilibrium existence results, J. Econ. Theory 102 (2002) 437–470] to games with possibly non-ordered preferences, providing a continuum analogue of the seminal existence results by Mas-Colell [An equilibrium existence theorem without complete or transitive preferences, J. Math. Econ. 1 (1974) 237–246], Gale and Mas-Colell [An equilibrium existence theorem for a general model without ordered preferences, J. Math. Econ. 2 (1975) 9–15], Shafer and Sonnenschein [Equilibrium in abstract economies without ordered preferences, J. Math. Econ. 2 (1975) 345–348], Borglin and Keiding [Existence of equilibrium actions and of equilibrium: a note on the “new” existence theorems, J. Math. Econ. 3 (1976) 313–316] and Yannelis and Prabhakar [Existence of maximal elements and equilibria in linear topological spaces, J. Math. Econ. 12 (1983) 233–245].     

Competitive equilibrium when preferences change over time

Summary. We show the existence of a competitive equilibrium in an economy with many consumers whose preferences may change over time. The demand correspondence of an individual consumer is determined by the set of subgame-perfect equilibrium outcomes in his intrapersonal game. For additively separable preferences with concave period utility functions that are unbounded above, this demand correspondence will satisfy the usual boundary conditions. Whenever consumers can recall their own mixed actions, this correspondence is convex-valued. This ensures the existence of a symmetric competitive equilibrium.Received: 29 July 2004, Revised: 17 November 2004, JEL Classification Numbers: D51, D91, C73. Correspondence to: Thomas MariottiWe thank Michele Piccione for useful comments and suggestions. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.     

Time-inconsistent preferences in a general equilibrium model

This paper introduces time-inconsistent preferences in a multicommodity general equilibrium framework with incomplete markets. The standard concept of competitive equilibrium is extended in order to allow for changes in intertemporal preferences. Depending on whether or not agents recognize that their intertemporal preferences change, agents are called sophisticated or naïve. This paper presents competitive equilibrium notions for economies with naïve agents and economies with sophisticated agents and provides assumptions under which both types of equilibria exist. Surprisingly, the set of naïve equilibria in societies populated by time-consistent households is not allocationally equivalent to the set of competitive equilibria. For sophisticated equilibria, the equivalence holds. Time-inconsistency also raises conceptual issues about the appropriate concept of efficiency. Choices have to be made concerning the incorporation of future preferences and the appropriate instruments to create Pareto improvements. For both naïve and sophisticated societies, we present four possible efficiency concepts. Suitable conditions are specified for which both naïve and sophisticated equilibria satisfy appropriate efficiency concepts.     

Evolutionary stability of discrimination under observability

We study the evolution of preferences under perfect and almost perfect observability in symmetric 2-player games. We demonstrate that if nature can choose from a sufficiently general preference space, which includes preferences over outcomes that may depend on the opponent's preference-type, then, in most games, only discriminating preferences (treating different types of opponents differently in the same situation) can be evolutionary stable and some discriminating types are stable in a very strong sense in all games. We use these discriminating types to show that any symmetric outcome which gives players more than their minmax value in material payoffs (fitness) can be seen as equilibrium play of a player population with such strongly stable preferences.     

The Dynamic Evolution of Preferences

This paper develops a general methodology for characterizing the dynamic evolution of preferences in a wide class of strategic interactions. We give simple conditions characterizing the limiting distribution of preferences in general games, and apply our results to study the evolutionary emergence of overconfidence and interdependent preferences. We also show that this methodology can be adapted to cases where preferences are only imperfectly observed. Earlier drafts of this paper were circulated under the title: “The Evolution of Perception Biases” and some of these results appeared in the earlier working paper Heifetz, Shannon and Spiegel (2003). We thank three anonymous referees for their helpful comments. Shannon thanks the NSF for research support under grant SES-0351346.     

Weighted congestion games with separable preferences

Players in a congestion game may differ from one another in their intrinsic preferences (e.g., the benefit they get from using a specific resource), their contribution to congestion, or both. In many cases of interest, intrinsic preferences and the negative effect of congestion are (additively or multiplicatively) separable. This paper considers the implications of separability for the existence of pure-strategy Nash equilibrium and the prospects of spontaneous convergence to equilibrium. It is shown that these properties may or may not be guaranteed, depending on the exact nature of player heterogeneity.     

Global asymptotic stability of a competitive equilibrium with recursive preferences

Summary. This paper demonstrates global stability of a competitive equilibrium in a multi-sector model of many firms, each of which exhibits constant returns to scale technology, and of infinitely lived consumers, whose preferences are recursive but not necessarily additively separable. In the topology induced by a sup-norm, the dominant diagonal blocks condition (Araujo and Scheinkman (Econometrica 45, 1977)) allows us to apply the implicit function theorem to obtain continuity of the equilibrium path. If a stationary equilibrium is locally asymptotically stable, then the continuity of the equilibrium path and smoothness of a weight function on heterogeneous consumers imply that all equilibrium paths converge to the steady state. The dominant diagonal blocks condition is also shown to be sufficient for the local asymptotic turnpike property. Received: December 13, 1996; revised version: June 2, 1999     

Heterogeneous preferences and investments in energy saving measures

We investigate whether risk, time, environmental, and social preferences affect single-family homeowners’ investments in the energy efficiency of their house using established experimental measures and questionnaires. We find that homeowners who report to be more risk taking are more likely to have renovated their house. Pro-environmental and future-oriented renovators, i.e. renovators with lower discount factors, live in homes with higher energy efficiency. Pro-social preferences as measured in a dictator game relates positively to the energy quality of renovated houses. Controlling for the energy efficiency of houses, we further find that energy consumption as measured by heating and electricity costs is lower for future-oriented and pro-environmental individuals.     

The lexicographic composition of abstract games

The lexicographic composition of reflexive and complete binary relations (which are often called abstract games) is studied. The necessary and sufficient conditions are obtained for a lexicographic composition of quasi transitive relations to be quasi transitive.The case of acyclicity of lexicographic composition of two relations is also investigated. Received: September 25, 2000; revised version: November 28, 2000     

Dynamic preferences and specialized tastes

A dynamic preference model suggests why people may develop specialized tastes as they age, why initially similar people may develop different specializations, and why socially related people, even if initially dissimilar, may develop the same specializations.     

Evolutionary dynamics on infinite strategy spaces

Summary. The study of evolutionary dynamics was so far mainly restricted to finite strategy spaces. In this paper we show that this unsatisfying restriction is unnecessary. We specify a simple condition under which the continuous time replicator dynamics are well defined for the case of infinite strategy spaces. Furthermore, we provide new conditions for the stability of rest points and show that even strict equilibria may be unstable. Finally, we apply this general theory to a number of applications like the Nash demand game, the War of Attrition, linear-quadratic games, the harvest preemption game, and games with mixed strategies. Received: June 25, 1999; revised version: January 31, 2000     

The evolutionary stability of constant consistent conjectures

In the general context of smooth two-player games, this paper shows that there is a close connection between (constant) consistent conjectures in a given game and the evolutionary stability of these conjectures. Evolutionarily stable conjectures are consistent and consistent conjectures are the only interior candidates to be evolutionarily stable. Examples are provided to illustrate the result.     

The relation of risk attitudes and other-regarding preferences: A within-subjects analysis

In this paper we provide experimental evidence on the relation of individual risk attitudes and subjects׳ aversion to favorable inequality. In a within-subjects design we expand Blanco et al.׳s (2011) modified dictator game by the risk-elicitation task of Eckel and Grossman (2002). Our data show strong support for a significant negative correlation between risk tolerance and an aversion to favorable inequality. The results are independent of gender, i.e., women and men show a similar correlation in these traits.     

连续进化金融模型与全局渐进化稳定策略

本文运用达尔文生物进化论思想研究连续交易金融市场选择的动态变化及一般均衡规律。本文发现并证明了:金融资产“赢利”的充要条件是该资产相对股息大于相对股价;投资比例等于股息分发比例的简单混合策略是全局渐近进化稳定策略;在均衡条件下,对应的金融资产价格等于该资产股息占总股息的比例的数学期望;市场变异或金融创新是有效市场形成的动力;全局渐近进化稳定策略业绩可能在某些时候不是最好的,但只要其初始财富大于零,最终将控制市场上的所有财富,而简单混合策略,可能在某个时候业绩优良,然而,在市场存在全局渐近进化稳定策略的条件下,只要其初始财富份额小于1,最终控制的财富趋向于零,从而被市场所淘汰。     

Self-Fulfilling Mechanisms in Bayesian Games

Amechanismfor a Bayesian gameGis a mapping μ from the set of states of nature to the set of players' actions. μ isself-fulfillingif players are truthful at the communication stage and, given the information revealed by μ, no player can gain in unilaterally deviating from the action prescribed by the mechanism. We investigate the properties of self-fulfilling mechanisms and we show in particular that they correspond to inert solutions of the infinitely repeated game generated byG. We also discuss applications to market games, regulation, and R&D games.Journal of Economic LiteratureClassification Numbers: D82, C72.