A comment on "The selection of preferences through imitation"

We observe that the imitation dynamics of Cubitt and Sugden (Review of Economic Studies, 1998, hereafter CS) is the same as the Replicator Dynamics for a certain class of games. Known results for such games then permit a more complete analysis of the CS imitation process, containing their results as special cases, and extending them considerably. We also offer a comment on the special role of "pure" prospects.Imitation

Ruling out multiplicity and indeterminacy: The role of heterogeneity.

It is well known that economies of scale that are external to the individual decision makers can lead to self-fulfilling prophecies and the multiplicity or even indeterminacy of equilibrium. We argue that the importance of this source of multiplicity and indeterminacy is overstated in representative agent models, as they ignore the potential stabilizing effect of heterogeneity. We illustrate this point in a version of Matsuyama' s (1991) two-sector model with increasing returns to scale. Two main results are shown. First, sufficient homogeneity with respect to individual productivity leads to the instability and non-uniqueness of a given stationary state and the indeterminacy of equilibrium at that stationary state. Second, sufficient heterogeneity leads to the global saddle-path stability and the uniqueness of a given stationary state and the global uniqueness of equilibrium.Heterogeneity; increasing returns to scale; indeterminacy; stability; uniqueness;

Think, but Not Too Much: A Dual-Process Model of Willpower and Self-Control

Dual-process theories view decisions as the result of the interaction of two qualitatively different types of processes, automatic/impulsive and controlled/deliberative. This paper considers a model of self-control where each decision can be taken by either an automatic process or a deliberative one. In line with recent evidence from psychology, effortful self-control (willpower) is modeled as a limited resource, i.e. exercising self-control for an initial decision limits the amount of self-control available for persevering later. Automatic decisions follow a reinforcement-based process, while controlled ones are utility-maximizing. A "personal evolution" approach shows that agents might fall into self-control traps: for instance, although exercising full self-control might be efficient, decision makers might be caught in a "personal optimum" where no self-control is exercised. Reciprocally, agents might also fall prey to excessive self-control, where they waste willpower in initial decisions only to give in to temptation later

The Logit-Response Dynamics

We develop a characterization of stochastically stable states for the logit-response learning dynamics in games, with arbitrary specification of revision opportunities. The result allows us to show convergence to the set of Nash equilibria in the class of best-response potential games and the failure of the dynamics to select potential maximizers beyond the class of exact potential games. We also study to which extent equilibrium selection is robust to the specification of revision opportunities. Our techniques can be extended and applied to a wide class of learning dynamics in games.Learning in games, logit-response dynamics, best-response potential games

Malliavin differentiability of the Heston volatility and applications to option pricing

We prove that the Heston volatility is Malliavin differentiable under the classical Novikov condition and give an explicit expression for the derivative. This result guarantees the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model. Furthermore we derive conditions on the parameters which assure the existence of the second Malliavin derivative of the Heston volatility. This allows us to apply recent results of the first author [3] in order to derive approximate option pricing formulas in the context of the Heston model. Numerical results are given.Malliavin calculus; stochastic volatility models; Heston model; Cox- Ingersoll-Ross process; Hull and White formula; Option pricing

Aromatic nitrations by mixed acid. Slow liquid-liquid reaction regime

Aromatic nitrations by mixed acid have been selected as a specific case of a heterogeneous liquid-liquid reaction. An extensive experimental programme has been followed using adiabatic and heat-flow calorimetry and pilot reactor experiments, supported by chemical analysis. A series of nitration experiments has been carried out to study the influences of different initial and operating conditions such as temperature, stirring speed and sulphuric acid concentration. In parallel, a mathematical model to predict the overall conversion rate has been developed. In this paper the mathematical modelling and the implementation and experimental validation for benzene, toluene and chlorobenzene mononitration in the kinetic control regime (slow liquid-liquid reaction) are presented and discussed

Suppression of Conductance in a Topological Insulator Nanostep Junction

We investigate quantum transport via surface states in a nanostep junction on the surface of a 3D topological insulator that involves two different side surfaces. We calculate the conductance across the junction within the scattering matrix formalism and find that as the bias voltage is increased, the conductance of the nanostep junction is suppressed by a universal factor of 1/3 compared to the conductance of a similar planar junction based on a single surface of a topological insulator. We also calculate and analyze the Fano factor of the nanostep junction and predict that the Fano factor saturates at 1/5, five times smaller than for a Poisson process

Does Backwards Induction Imply Subgame Perfection?

In finite games subgame perfect equilibria are precisely those that are obtained by a backwards induction procedure. In large extensive form games with perfect information this equivalence does not hold: Strategy combinations fulfilling the backwards induction criterion may not be subgame perfect in general. The full equivalence is restored only under additional (topological) assumptions. This equivalence is in the form of a one-shot deviation principle for large games, which requires lower semi-continuous preferences. As corollaries we obtain one-shot deviation principles for particular classes of games, when each player moves only finitely often or when preferences are representable by payoff functions that are continuous at infinity