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, i.e. 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.

We study the representative consumer's risk attitude and efficient risk-sharing rules in a single-period, single-good economy in which consumers have homogeneous probabilistic beliefs but heterogeneous risk attitudes. We prove that if all consumers have convex absolute risk tolerance, so must the representative consumer. We also identify a relationship between the curvature of an individual consumer's individual risk sharing rule and his absolute cautiousness, the first derivative of absolute risk-tolerance. Furthermore, we discuss some consequences of these results and refinements of these results for the class of HARA utility functions.

Nöldeke and Samuelson (1993) investigate a stochastic evolutionary model for extensive form games and show that even for games of perfect information with a unique subgame perfect equilibrium, non-subgame perfect equilibrium-strategies may well survive in the long run even when mutation rates tend to zero. In a different model of evolution in the agent normal form of these games Hart (2002) shows that under suitable limit-taking, where small mutation rates are accompanied by large population sizes in a particular way, the unique prediction is again the subgame perfect equilibrium. This paper provides a proof of a similar result for the model of Nöldeke and Samuelson (1993).

The empirical joint distribution of return pairs on stock indices displays high tail-dependence in the lower tail and low tail-dependence in the upper tail. The presence of tail-dependence is not compatible with the assumption of (conditional) joint normality. The presence of asymmetric tail-dependence is not compatible with the assumption of a joint student-t distribution. A general test for one dependence structure versus another via the profile likelihood is described and employed in a bivariate GARCH model, where the joint distribution of the disturbances is split into its marginals and its copula. The copula used in the paper is such that it allows for the existence of lower tail-dependence and for asymmetric tail-dependence, and is such that it encompasses the normal or t-copula, depending on the benchmark tested. The model is estimated using bivariate data on a set of European stock indices. We find that the assumption of normal or student-t dependence is easily rejected in favour of an asymmetrically tail-dependent distribution.

This paper deals with optimal window width choice in non-parametric lag or spectral window estimation of the spectral density of a stationary zero-mean process. Several approaches are reviewed: cross-validation-based methods as described by Hurvich (1985), Beltrão& Bloomfield (1987) and Hurvich & Beltrão (1990); an iterative procedure developed by Bühlmann (1996); and a bootstrap approach followed by Franke & Härdle (1992). These methods are compared in terms of the mean square error, the mean square percentage error, and a third measure of the distance between the true spectral density and its estimate. The comparison is based on a simulation study, the simulated processes being in the class of ARMA(5,5) processes. On the basis of simulation evidence we suggest to use a slightly modified version of Bühlmann's (1996) iterative method. This paper also makes a minor correction of the bootstrap criterion by Franke & Härdle (1992).

We study the potential evolutionary appeal of rationality in a model in which different populations differ with respect to their experimentation over new rules of behavior. We find that experimentation over the set of (strictly) rational rules dominates any other form of experimentation. This evolutionary advantage of strict rationality, furthermore, is substantial when learning takes place over a limited amount of time, or when the environment is stochastically changing.

We provide a general formal framework to define and analyze the concepts of focal points and frames for normal form games. The information provided by a frame is captured by a symmetry structure which is consistent with the payoff structure of the game. The set of alternative symmetry structures has itself a clear structure (a lattice). Focal points are strategy profiles which respect the symmetry structure and are chosen according to some meta-norm, which is not particular to the framed game at hand. The definition of a symmetry structure is given in steps of increasing complexity allowing us to precisely explain differences between existing definitions.

We characterize the smallest faces of the polyhedron of strategy profiles that could possibly be made asymptotically stable under some reasonable deterministic dynamics. These faces are Kalai and Samet's (1984) persistent retracts and are spanned by Basu and Weibull's (1991) CURB sets based on a natural (and, in a well-defined sense, minimal) refinement of the best-reply correspondence. We show that such a correspondence satisfying basic properties such as existence, upper hemi-continuity, and convex-valuedness exists and is unique in most games. We introduce a notion of rationalizability based on this correspondence and its relation to other such concepts. We study its fixed-points and their relations to equilibrium refinements. We find, for instance, that a fixed point of the refined best reply correspondence in the agent normal form of any extensive form game constitutes a perfect Bayesian equilibrium, which is weak perfect Bayesian in every subgame. Finally, we study the index of its fixed point components.

In an exchange economy in which there is a complete set of markets for macroeconomic risks but no market for idiosyncratic risks, we consider how the efficient risk-sharing rules for the macroeconomic risk are affected by the heterogeneity in the consumers' risk attitudes and idiosyncratic risks. We provide sufficient conditions under which an idiosyncratic risk increases cautiousness (the derivative of the reciprocal of the absolute risk aversion), the determinant of the curvatures of the efficient risk-sharing rules. While the curvature of the risk-sharing rules at high consumption levels are governed by the consumers' risk attitudes, the curvature at low consumption levels depend not only on the risk attitudes but also on the lower tail distributions of the idiosyncratic risks.

This paper analyzes a stochastic best reply evolutionary model with inertia in normal form games. The long-run behavior of individuals in this model is investigated in the limit where experimentation rates tend to zero, while the expected number of experimenters, and hence also population sizes, tend to infinity. Conditions on the learning-rate which are necessary and sufficient for the evolutionary elimination of weakly dominated strategies are found. The key determinant is found to be the sensitivity of the learning-rate to small payoff differences.

Within a standard stochastic evolutionary framework, we study the evolution of morality, both at the level of behavior and at the level of codes of behavior. These moral codes involve sanctioning deviant agents. We provide conditions under which the presence of inter- roup conflict allows the emergence of moral codes which improve social efficiency. The result depends on both the efficacy of the available sanctioning technology and on the ratio of the number of societies and the number of members which societies are composed of. We also consider the possibility that a moral code involves rewards rather than sanctions. We show that, in contrast with sanctioning moral codes, no system of rewards will evolve and therefore social efficiency cannot be improved via this mechanism.

A population of individuals is divided into groups. Individuals are recurrently randomly matched with individuals from their group to play a generic symmetric 2-player game. Deterministic inter- and intra-group dynamics are derived from a model of individual imitation within groups and individual migration between groups. Conditions are identified under which subsets (components) of the set of stationary states are (interior) asymptotically stable. The results are then applied to generic coordination games and the prisoners' dilemma. The unique asymptotically stable set of stationary states in coordination games is such that every individual in non-extinct groups plays the Pareto-optimal equilibrium. In the multi-group prisoners' dilemma there is no asymptotically stable subset of the set of stationary states.