Options can induce risk taking for arbitrary preferences

Summary. It is widely believed that call options induce risk-taking behavior. However, Ross (2004) challenges this intuition by demonstrating the impossibility of inducing managers with arbitrary preferences to always act as if they were less risk averse. If preferences and price distributions are unknown, risk-taking behavior cannot be always induced by an option contract. Here, we prove a new result showing that, with no information about preferences and some knowledge about prices, one can write a call option that makes all managers prefer riskier projects to safer ones. This points out that in order to design options that induce risk taking it is sufficient to have information about price distributions.Received: 5 November 2003, Revised: 1 November 2004, JEL Classification Numbers: D81, G00, J33, M21. Correspondence to: Luis H.B. BraidoWe thank Renée Adams, Heitor Almeida, Carlos E. da Costa, Andrew Horowitz, Paulo K. Monteiro, Walter Novaes, Sergio O. Parreiras, Rodrigo R. Soares, and especially Marcos Tsuchida for many helpful comments.     

Payoff dominance and risk dominance in the observable delay game: a note

We examine whether the payoff dominant sequential-move (Stackelberg) outcome is realized when timing is endogenized. We adopt the observable delay game formulated by Hamilton and Slutsky [Games Econ Behav 2(1):29–46, 1990]. We find that if one sequential-move outcome is payoff dominant, either (i) the outcome both players prefer is the unique equilibrium; or (ii) two sequential-move outcomes are equilibria and the one both players prefer is risk dominant. In other words, no conflict between payoff dominance and risk dominance in the observable delay game exists, in contrast to other games such as (non pure) coordination games. We also find that even if one of two sequential-move outcomes is the unique equilibrium outcome in the observable delay game, it does not imply that the equilibrium outcome is payoff dominant to the other sequential-move outcome.      

Equilibrium uniqueness with perfect complements

The present note analyzes the simultaneous ascending-bid auction with arbitrarily many asymmetric bidders with decreasing marginal valuations under complete information. We show that the game is solvable by iterated elimination of weakly dominated strategies if the efficient allocation assigns at least one unit to every player and if bid increments are sufficiently small. In that unique equilibrium, bidders immediately reduce their demand to the efficient allocation, and the auction ends in the first round of bidding.We would like to thank seminar participants at UC Davis, in particular Klaus Nehring and Louis Makowski for comments. Financial support by the Alexander–von–Humboldt Foundation through a Feodor–Lynen grant and by the Deutsche Forschungsgemeinschaft, SFB Transregio 15, “Governance and Efficiency of Economic Systems” is gratefully acknowledged.     

On forward induction in money-burning games

Summary. We first consider money-burning games studied by Ben-Porath and Dekel [6]. We show that iterative weak dominance and extensive form rationalizability yield the same unique outcome in this class of games. This result suggests that weak dominance captures the forward induction logic implied by extenisve form rationalizability. Next, we consider an example of entry model by Arvan [1] to demonstrate the power of forward induction. In this example, despite the presence of multiple equilibria, forward induction chooses a unique outcome. Received: January 25, 2000; revised version: January 5, 2001     

Incentive monotonicity and equilibrium selection in 2×2 matrix games

For the class of 2×2 matrix games with two strict Nash equilibria the paper introduces an equilibrium refinement called incentive monotonicity. It selects the risk-dominant equilibrium if interests are conflicting, while it remains silent in games with common interests. These results suggest that the equilibrium-selection problem might be more difficult in games with common interests, which is certainly the case if risk dominance and payoff dominance go in opposite directions.     

Equilibrium selection through incomplete information in coordination games: an experimental study

We perform an experiment on a pure coordination game with uncertainty about the payoffs. Our game is closely related to models that have been used in many macroeconomic and financial applications to solve problems of equilibrium indeterminacy. In our experiment, each subject receives a noisy signal about the true payoffs. This game (inspired by the “global” games of Carlsson and van Damme, Econometrica, 61, 989–1018, 1993) has a unique strategy profile that survives the iterative deletion of strictly dominated strategies (thus a unique Nash equilibrium). The equilibrium outcome coincides, on average, with the risk-dominant equilibrium outcome of the underlying coordination game. In the baseline game, the behavior of the subjects converges to the theoretical prediction after enough experience has been gained. The data (and the comments) suggest that this behavior can be explained by learning. To test this hypothesis, we use a different game with incomplete information, related to a complete information game where learning and prior experiments suggest a different behavior. Indeed, in the second treatment, the behavior did not converge to equilibrium within 50 periods in some of the sessions. We also run both games under complete information. The results are sufficiently similar between complete and incomplete information to suggest that risk-dominance is also an important part of the explanation.      

The impact of prudence on optimal prevention

Summary. What are the determinants of the optimal level of effort to reduce the probability of a loss to occur? Whereas most of the literature on this question focused on risk aversion, we show that the concept of prudence (i.e., a positive third derivative of the utility function) is essential to answer this question. We explain in this paper that prudence and prevention tend to be opponents rather than allies contrary to the intuition attached to everyday language.Received: 7 November 2003, Revised: 3 August 2004, JEL Classification Numbers: D61, D81. Correspondence to: Christian Gollier     

Inequality of Happiness in the U.S.: 1972–2010

It is well accepted that a country's GDP may not fully reflect its level of well‐being. In recent years, happiness has emerged as an alternative indicator of well‐being, and research has mainly focused on determining the level of happiness. While it is important to look at the level, the distribution of happiness is also a salient aspect in any evaluation of inequality. There has been a growing interest in the distribution of happiness, although the ordinal nature of the data makes the use of standard inequality measures problematic. Our paper contributes to the literature by exploring the distributions for the U.S. from 1972 to 2010. Based on new methods developed for ordinal data, we are able to overcome the problems associated with ordinality and obtain unambiguous rankings of happiness distributions. We also compute the level of happiness inequality using existing measures based on median centred approaches. Further, we decompose the median based inequality measures of happiness by gender, race, and region.     

Playing Cournot although they shouldn’t

Summary. In this note, we experimentally investigate the extended game with action commitment in a Cournot duopoly with asymmetric cost. Risk dominance considerations allow to select a unique equilibrium in which the low-cost firm is the Stackelberg leader. The data, however, do not support the theory as simultaneous-move play is modal. Average output choices are in line with the Cournot equilibrium. This suggests that Cournot is a much more robust predictor for competition in markets than theory suggests.Received: 14 October 2002, Revised: 1 December 2003, JEL Classification Numbers: C72, C92, D43. Correspondence to: Hans-Theo Normann     

Measuring the severity of unemployment

A social-welfare (illfare) function framework is applied to compare two demographic groups as to the severity of their unemployment experience. This is based on the assumption that for each individual the disutility of unemployment is an increasing and convex function of spell length. The very concept of spell length and its distribution, however, is not unambiguous. In contrast to previous literature which focuses exclusively on the interrupted spell length in a stock of unemployed, we stress the usefulness of the concept of complete spell length in a cohort of unemployed. We establish an equivalence relationship between second-degree dominance in the cohort and first-degree dominance in the stock. For specific illfare functions the disutilityU(x) when applied to the cohort and the disutilityU(x) when applied to the stock will produce the same value of aggregate welfare (illfare).     

Strategic Similarity and Emergent Conventions: Evidence from Similar Stag Hunt Games

This paper reports evidence on the origin of convention in laboratory cohorts confronting similar but not identical strategic situations repeatedly. The experiment preserves the action space of the game, while randomly perturbing the payoffs and scrambling the action labels in an effort to blunt the salience of retrospective selection principles. Hence, the similarity between stage games is reduced to certain strategic details, like efficiency, security, and risk dominance. Nevertheless, we do observe conventions emerging in half of the laboratory cohorts. When a convention emerges subjects's behavior conforms to the selection principles of efficiency rather than security or risk dominance. Journal of Economic Literature Classification Numbers: C72, C78, C92, D83.     

Satisficing and optimality in 2×2 common interest games

Summary. The paper studies the evolution of cooperation when satisficing players repeatedly play a symmetric two-by-two game of common interest. We show that if initial aspiration levels are sufficiently close to the efficient payoff and aspiration adjusts at a sufficiently slow speed then the unique long run state will be the efficient outcome. In the special case of coordination games, the more tension there is between payoff dominance and risk dominance, the longer it takes for the system to lock into the payoff dominant outcome. Received: June 23, 1997; revised version: November 19, 1997     

Network formation and social coordination

This paper develops a simple model to examine the interaction between partner choice and individual behavior in games of coordination. An important ingredient of our approach is the way we model partner choice: we suppose that a player can establish ties with other players by unilaterally investing in costly pairwise links. In this context, individual efforts to balance the costs and benefits of links are shown to lead to a unique equilibrium interaction architecture. The dynamics of network formation, however, has powerful effects on individual behavior: if costs of forming links are below a certain threshold then players coordinate on the risk-dominant action, while if costs are above this threshold then they coordinate on the efficient action. These findings are robust to modifications in the link formation process, different specifications of link formation costs, alternative models of mutations as well as the possibility of interaction among indirectly connected players.     

Arrow's Possibility Theorem for one-dimensional single-peaked preferences

In one-dimensional environments with single-peaked preferences we consider social welfare functions satisfying Arrow's requirements, i.e. weak Pareto and independence of irrelevant alternatives. When the policy space is a one-dimensional continuum such a welfare function is determined by a collection of 2^N strictly quasi-concave preferences and a tie-breaking rule. As a corollary we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave.     

Stochastic dominance and decomposable measures of inequality and poverty

In this paper, we characterize some new links between stochastic dominance and the measurement of inequality and poverty. We show that: for second-degree normalized stochastic dominance (NSD), the weighted area between the NSD curve of a distribution and that of the equalized distribution is a decomposable inequality measure; for first-degree and second-degree censored stochastic dominance (CSD), the weighted area between the CSD curve of a distribution and that of the zero-poverty distribution is a decomposable poverty measure. These characterizations provide graphical representations for decomposable inequality and poverty measures in the same manner as Lorenz curve does for the Gini index. The extensions of the links to higher degrees of stochastic dominance are also investigated.     

On the Relationship between Risk-Dominance and Stochastic Stability

In a 2 × 2 symmetric game with two symmetric equilibria, one risk-dominates another if and only if the equilibrium strategy is a unique best response to any mixture that gives itself at least a probability of one-half. In a two-person strategic form game, we call a Nash equilibriumglobally risk-dominantif it consists of strategies such that each one of them is a unique best response to any mixture that gives the other at least a probability of one-half. We show that if a weakly acyclic two-person game has a globally risk-dominant equilibrium, then this is the one that is selected by the stochastic equilibrium selection process of Young.Journal of Economic LiteratureClassification Numbers: C72, C73.     

Learning with noiseless information and payoff-relevant signals

Summary. In models of active learning or experimentation, agents modify their actions to affect the distribution of a signal that provides information about future payoffs. A standard result in the experimentation literature is that agents experiment, if at all, to increase information. This finding is a direct consequence of Blackwell's theorem: one experiment is more informative than another if and only if all expected utility maximizers prefer to observe the first. Blackwell's theorem presupposes, however, that the observed signal only conveys information and does not directly affect future payoffs. Often, however, signals are directly payoff relevant, a phenomenon that we call signal dependence. For example, if a firm is uncertain about its demand and uses today's sales as a signal of tomorrow's demand, then that signal may also directly affect tomorrow's profit if the good is durable or if consumers form consumption habits. Datta, Mirman and Schlee [9] and Bertocchi and Spagat [4] show that, if the signal is payoff relevant, experimentation may indeed reduce information. Here we show that, despite the inapplicability of Blackwell's Theorem, agents always experiment to increase information if the information structure is noiseless: given the true value of the unknown parameter, the signal realization is deterministic. We then apply our framework to analyze Lazear's [16] model of retail clearance sales, a model with both signal dependence and noiseless information. Received: February 19, 1999; revised version: August 11, 1999     

Market integration between wild and farmed seabream and seabass in Spain

Gilthead seabream (Sparus aurata) and European seabass (Dicentrarchus labrax) production from aquaculture has been increasing since the 1990s. Nowadays, about 95% of their production comes from aquaculture. In this study, we analyse if the rapid growth in the aquaculture production of both species has affected the capture fisheries prices of both species. In other words, we investigate if there is market integration between wild and farmed gilthead seabream and European seabass. In order to do this analysis, we use data from the main gilthead seabream and European seabass markets in Spain. The results show that there is no market integration between wild and farmed gilthead seabream and European seabass. This implies that capture fisheries are not affected by increases in the aquaculture production of both species. But gilthead seabream and European seabass aquaculture producers face a smaller demand that explains the difficulties this aquaculture segment is facing.     

Adaptive Learning and Iterated Weak Dominance

This article addresses the idea that rational players should not play iteratively weakly dominated strategies by showing that when a particular type of adaptive learning process converges, then players must have learned to play strategy profiles equivalent to those that survive iterated nice weak dominance and, for certain games, equivalent to those that survive iterated weak dominance. For games satisfying the weak single crossing condition, the set of strategies that survive iterated weak dominance is small in that its bounds are pure strategy Nash equilibria. The results hold regardless of the order in which dominated strategies are eliminated.Journal of Economic LiteratureClassification Number: C72.