Dispersion Size-Consistency

A multivariate adiabatic connection (MAC) framework for describing dispersion interactions in a system consisting of non-overlapping monomers is presented. By constraining the density to the physical ground-state density of the supersystem, the MAC enables a rigorous separation of induction and dispersion effects. The exact dispersion energy is obtained from the zero-temperature fluctuation-dissipation theorem and partitioned into increments corresponding to the interaction energy gained when an additional monomer is added to a -monomer system. The total dispersion energy of an -monomer system is independent of any partitioning into subsystems. This statement of dispersion size consistency is shown to be an exact constraint. The resulting additive separability of the dispersion energy results from multiplicative separability of the generalized screening factor defined as the inverse generalized dielectric function. Many-body perturbation theory (MBPT) is found to violate dispersion size-consistency because perturbative approximations to the generalized screening factor are nonseparable; on the other hand, random phase approximation-type methods produce separable generalized screening factors and therefore preserve dispersion size-consistency. This result further explains the previously observed increase in relative errors of MBPT for dispersion interactions as the system size increases. Implications for electronic structure theory and applications to supramolecular materials and condensed matter are discussed.

Behavioral Theory of Repeated Prisoner’s Dilemma: Generous Tit-For-Tat Strategy

This study investigates infinitely repeated games of a prisoner’s dilemma with additive separability in which the monitoring technology is imperfect and private. Behavioral incentives indicate that a player is not only motivated by pure self-interest but also by social preference such as reciprocity, and that a player often becomes naïve and selects an action randomly due to her cognitive limitation and uncertain psychological mood as well as the strategic complexity caused by monitoring imperfection and private observation. By focusing on generous tit-for-tat strategies, we characterize a behavioral version of Nash equilibrium termed behavioral equilibrium in an accuracy-contingent manner. By eliminating the gap between theory and evidence, we show that not pure self-interest but reciprocity plays a substantial role in motivating a player to make decisions in a sophisticated manner.

ON THE COMPLETENESS CONDITION IN NONPARAMETRIC INSTRUMENTAL PROBLEMS

The notion of completeness between two random elements has been considered recently to provide identification in nonparametric instrumental problems. This condition is quite abstract, however, and characterizations have been obtained only in special cases. This paper considers a nonparametric model between the two variables with an additive separability and a large support condition. In this framework, different versions of completeness are obtained, depending on which regularity conditions are imposed. This result allows one to establish identification in an instrumental nonparametric regression with limited endogenous regressor, a case where the control variate approach breaks down.