Christoph Kuzmics

Tail-dependence in stock-return pairs

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 is such that it allows for the presence of lower tail-dependence and for asymmetric tail-dependence, and that it encompasses the normal or t-copula. 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.

Representative consumer's risk aversion and efficient risk-sharing rules

We study the representative consumers 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 consumers 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.

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 opponents 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.

Symmetric Play in Repeated Allocation Games

We study symmetric play in a class of repeated games when players are patient. We show that, while the use of symmetric strategy profiles essentially does not restrict the set of feasible payoffs, the set of equilibrium payoffs is an interesting proper subset of the feasible and individually rational set. We also provide a theory of how rational individuals play these games, identifying particular strategies as focal through the considerations of Pareto optimality and simplicity. We report experiments that support many aspects of this theory.

Effects of Background Risks on Cautiousness with an Application to a Portfolio Choice Problem

We provide necessary and sufficient conditions on an individuals expected utility function under which any zero-mean idiosyncratic risk increases cautiousness (the derivative of the reciprocal of the absolute risk aversion), which is the key determinant for this individuals demand for options and portfolio insurance.

Refined best reply correspondence and dynamics

We call a correspondence, defined on the set of mixed strategy profiles, a generalized best reply correspondence if it has a product structure, is upper hemi-continuous, always includes a best reply to any mixed strategy profile, and is convex- and closed-valued. For each generalized best reply correspondence we define a generalized best reply dynamics as a differential inclusion based on it. We call a face of the set of mixed strategy profiles a minimally asymptotically stable face (MASF) if it is asymptotically stable under some such dynamics and no subface of it is asymptotically stable under any such dynamics. The set of such correspondences (and dynamics) is endowed with the partial order of point-wise set-inclusion and, under a mild condition on the normal form of the game at hand, forms a complete lattice with meets based on point-wise intersections. The refined best reply correspondence is then defined as the smallest element of the set of all generalized best reply correspondences. We ultimately find that every Kalai and Samets (1984) persistent retract, which coincide with Basu and Weibulls (1991) CURB sets based, however, on the refined best reply correspondence, contains a MASF. Conversely, every MASF must be a Voornevelds (2004) prep set, again, however, based on the refined best reply correspondence.

Refined best reply correspondence and dynamics: Best reply correspondence and dynamics

We call a correspondence, defined on the set of mixed strategy profiles, a generalized best reply correspondence if it (i) has a product structure, (ii) is upper hemicontinuous, (iii) always includes a best reply to any mixed strategy profile, and (iv) is convex- and closed-valued. For each generalized best reply correspondence, we define a generalized best reply dynamics as a differential inclusion based on it. We call a face of the set of mixed strategy profiles a minimally asymptotically stable face (MASF) if it is asymptotically stable under some such dynamics and no subface of it is asymptotically stable under any such dynamics. The set of such correspondences (and dynamics) is endowed with the partial order of pointwise set inclusion and, under a mild condition on the normal form of the game at hand, forms a complete lattice with meets based on pointwise intersections. The refined best reply correspondence is then defined as the smallest element of the set of all generalized best reply correspondences. We find that every persistent retract (Kalai and Samet 1984) contains a MASF. Furthermore, persistent retracts are minimal CURB (closed under rational behavior) sets (Basu and Weibull 1991) based on the refined best reply correspondence. Conversely, every MASF must be a prep set (Voorneveld 2004), based again, however, on the refined best reply correspondence.

Refined best-response correspondence and dynamics

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 Samets (1984) persistent retracts and are spanned by Basu and Weibulls (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.

The Refined Best-Response Correspondence in Normal Form Games

This paper provides an in-depth study of the (most) refined best-response correspondence introduced by Balkenborg et al. (Theor Econ 8:165–192, 2013). An example demonstrates that this correspondence can be very different from the standard best-response correspondence. In two-player games, however, the refined best-response correspondence of a given game is the same as the best-response correspondence of a slightly modified game. The modified game is derived from the original game by reducing the payoff by a small amount for all pure strategies that are weakly inferior. Weakly inferior strategies, for two-player games, are pure strategies that are either weakly dominated or are equivalent to a proper mixture of pure strategies. Fixed points of the refined best-response correspondence are not equivalent to any known Nash equilibrium refinement. A class of simple communication games demonstrates the usefulness and intuitive appeal of the refined best-response correspondence.

A comment on “Egalitarianism and efficiency in repeated symmetric games” by V. Bhaskar [Games Econ. Behav. 32 (2000) 247–262]☆

Abstract We identify an error in Bhaskarʼs (2000) Proposition 4. We provide counterexamples to this result and demonstrate that it is not correctable.