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.     

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].     

Undominated (and) perfect equilibria in Poisson games

In games with population uncertainty some perfect equilibria are in dominated strategies. We prove that every Poisson game has at least one perfect equilibrium in undominated strategies.     

Mixed-strategy equilibria and strong purification for games with private and public information

This paper shows the existence of mixed-strategy equilibria for games with private and public information under general conditions. Under the additional assumptions of finiteness of action spaces and diffuseness and conditional independence of private information, a strong purification result is obtained for the mixed strategies in such games. As a corollary, the existence of pure-strategy equilibria follows. I am very grateful to Yeneng Sun, Nicholas C. Yannelis and M. Ali Khan for helpful discussions and suggestions. I also wish to thank an anonymous referee whose comments led to many improvements in the paper.     

Mixed equilibria in games of strategic complementarities

Summary. The literature on games of strategic complementarities (GSC) has focused on pure strategies. I introduce mixed strategies and show that, when strategy spaces are one-dimensional, the complementarities framework extends to mixed strategies ordered by first-order stochastic dominance. In particular, the mixed extension of a GSC is a GSC, the full set of equilibria is a complete lattice and the extremal equilibria (smallest and largest) are in pure strategies. The framework does not extend when strategy spaces are multi-dimensional. I also update learning results for GSC using stochastic fictitious play. Received: October 16, 2000; revised version: March 7, 2002 RID="*" ID="*" I am very grateful to Robert Anderson, David Blackwell, Aaron Edlin, Peter De Marzo, Ted O'Donoghue, Matthew Rabin, Ilya Segal, Chris Shannon, Clara Wang and Federico Weinschelbaum for comments and advise.     

Perfect communication equilibria in repeated games with imperfect monitoring

This paper introduces an equilibrium concept called perfect communication equilibrium for repeated games with imperfect private monitoring. This concept is a refinement of Myerson's [Myerson, R.B., 1982. Optimal coordination mechanisms in generalized principal agent problems, J. Math. Econ. 10, 67–81] communication equilibrium. A communication equilibrium is perfect if it induces a communication equilibrium of the continuation game, after every history of messages of the mediator. We provide a characterization of the set of corresponding equilibrium payoffs and derive a Folk Theorem for discounted repeated games with imperfect private monitoring.     

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.     

Correlated equilibria in continuous games: Characterization and computation

We present several new characterizations of correlated equilibria in games with continuous utility functions. These have the advantage of being more computationally and analytically tractable than the standard definition in terms of departure functions. We use these characterizations to construct effective algorithms for approximating a single correlated equilibrium or the entire set of correlated equilibria of a game with polynomial utility functions.     

The envelope theorem for locally differentiable Nash equilibria of finite horizon differential games

Envelope theorems are established for a ubiquitous class of finite horizon differential games. The theorems cover open-loop and feedback information patterns in which the corresponding Nash equilibria are locally differentiable with respect to the parameters of the game. Their relationship with extant envelope results is discussed and an application of them to a generalized capital accumulation game is provided. An important implication of the theorems is that, in general, the archetypal economic interpretation of the costate vector, namely, as the shadow value of the state vector along the Nash equilibrium, is valid for feedback Nash equilibria, but not for open-loop Nash equilibria.     

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.     

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.     

Real estate and relative risk aversion with generalized recursive preferences

This paper investigates how real estate wealth affects the household’s attitude toward risk, and derives the closed-form expressions for risk aversion with generalized recursive preferences. We find three channels through which real estate wealth affects risk aversion, and these channels are absent in the traditional measure of relative risk aversion as in Arrow (1965) and Pratt (1964). First, illiquidity and fluctuations in real estate value increase consumption risk, thereby increasing risk aversion. Second, real estate as an asset provides a cushion for absorbing negative shocks to households, reducing risk aversion. Third, an increase in real estate prices lowers the profit of the firm that uses real estate as a factor of production, induces a decline in the real wage, and causes a rise in consumption risk. This channel increases risk aversion. We study how these channels as a whole determine relative risk aversion using a basic real business cycle model with generalized recursive preferences and compare the results with the case of expected utility preferences. Finally, we explore the implications of the firm’s and the household’s real estate holdings and illiquidity of real estate on the risk premiums for equity and real estate.     

“Very Nice” trivial equilibria in strategic market games

Following Shapley [Theory of Measurement of Economic Externalities, Academic Press, New York, 1976], we study the problem of the existence of a Nash Equilibrium (NE) in which each trading post is either active or “legitimately” inactive, and we call it a Shapley NE. We consider an example of an exchange economy, borrowed from Cordella and Gabszewicz [Games Econ. Behav. 22 (1998) 162–169], which satisfies the assumptions of Dubey and Shubik [J. Econ. Theory 17 (1978) 1–20], and we show that the trivial equilibrium, the unique NE of the associated strategic market game, is not “very nice,” in the sense that it is not “legitimately” trivial. This result has the more general implication that, under the Dubey and Shubik's assumptions, a Shapley NE may fail to exist.     

The possibility of mixed-strategy equilibria with constant-returns-to-scale technology under Bertrand competition

Abstract. We analyze the Nash equilibria of a standard Bertrand model. We show that in addition to the marginal-cost pricing equilibrium there is a possibility for mixed-strategy equilibria yielding positive profit levels. We characterize these equilibria and find that having unbounded revenues is the necessary and sufficient condition for their existence. Hence, we demonstrate that under realistic assumptions the only equilibrium is marginal-cost pricing.     

Inducing risk preferences in multi-stage multi-agent laboratory experiments

Though there has been some debate over the practical efficacy of using binary lotteries for controlling risk preferences in experimental environments, the question of its theoretical validity within the contexts it is often used, namely multi-stage multi-agent settings, has not been addressed. Whilst the original proof of its validity featured a single-agent single-stage context, its practical use has seen a wide range of implementations. Practitioners have implicitly assumed that whenever the setting and form of implementation they have chosen deviates from the original single-agent single-period proof, it remains theoretically valid. There has been virtually no debate in the practitioner literature on the theoretical validity of binary lotteries in a more general context, or on whether the form of implementation matters. The current article addresses these questions, establishes limitations on validity and suggests some design principles for future implementation of binary lotteries for the purpose of controlling risk preferences.     

A differentiable homotopy to compute Nash equilibria of n-person games

Summary. The literature on the computation of Nash equilibria in n-person games is dominated by simplicial methods. This paper is the first to introduce a globally convergent algorithm that fully exploits the differentiability present in the problem. It presents an everywhere differentiable homotopy to do the computations. The homotopy path can therefore be followed by several numerical techniques. Moreover, instead of computing some Nash equilibrium, the algorithm is constructed in such a way that it computes the Nash equilibrium selected by the tracing procedure of Harsanyi and Selten. As a by-product of our proofs it follows that for a generic game the tracing procedure defines a unique feasible path. The numerical performance of the algorithm is illustrated by means of several examples. Received: December 21, 1999; revised version: December 27, 2000     

Edgeworth and Walras equilibria of an arbitrage-free exchange economy

Summary. In this paper, we first give a direct proof of the existence of Edgeworth equilibria for exchange economies with consumption sets which are (possibly) unbounded below. The key assumption is that the individually rational utility set is compact. It is worth noticing that the statement of this result and its proof do not depend on the dimension or the particular structure of the commodity space. In a second part of the paper, we give conditions under which Edgeworth allocations can be decentralized by continuous prices in a finite dimensional and in an infinite dimensional setting. We then show how these results apply to some finance models.Received: 15 April 2002, Revised: 25 February 2003, JEL Classification Numbers: C62, D58, G12. Correspondence to: Monique FlorenzanoThis paper was presented at seminars of the Economic Departments of Brown University, The Johns Hopkins University, The University of Alabama, Purdue University and at the Centro de Modelamiento Matematico de la Universidad de Chile at Santiago. The paper has benefitted of the comments of these diverse audiences. Part of this work was done while the authors were visiting respectively Brown University and the Centro de Modelamiento Matematico. We thank them for their hospitality.     

The geometry of distributional preferences and a non-parametric identification approach: The Equality Equivalence Test

This paper proposes a geometric delineation of distributional preference types and a non-parametric approach for their identification in a two-person context. It starts with a small set of assumptions on preferences and shows that this set (i) naturally results in a taxonomy of distributional archetypes that nests all empirically relevant types considered in previous work; and (ii) gives rise to a clean experimental identification procedure – the Equality Equivalence Test – that discriminates between archetypes according to core features of preferences rather than properties of specific modeling variants. As a by-product the test yields a two-dimensional index of preference intensity.