Relativistic Internally Contracted Multireference Electron Correlation Methods

We report internally contracted relativistic multireference configuration interaction (ic-MRCI), complete active space second-order perturbation (CASPT2), and strongly contracted n-electron valence state perturbation theory (NEVPT2) on the basis of the four-component Dirac Hamiltonian, enabling accurate simulations of relativistic, quasi-degenerate electronic structure of molecules containing transition-metal and heavy elements. Our derivation and implementation of ic-MRCI and CASPT2 are based on an automatic code generator that translates second-quantized ansatze to tensor-based equations, and to efficient computer code. NEVPT2 is derived and implemented manually. The rovibrational transition energies and absorption spectra of HI and TlH are presented to demonstrate the accuracy of these methods

Relationships between Non-Bossiness and Nash Implementability

We explore the relationships between non-bossiness and Nash implementability. We provide a new domain-richness condition, weak monotonic closedness, and prove that on weakly monotonically closed domains, non-bossiness together with individual monotonicity is equivalent to monotonicity, a necessary condition for Nash implementation. The result shows an impossibility of Nash implementation in all economies except pure public goods economies, in the sense that it indicates that in all economies except pure public goods economies, it is impossible to implement bossy social choice functions in Nash equilibria, which embody the characteristics inherent in those economies.Non-Bossiness, Individual Monotonicity, Monotonicity, Weak Monotonic Closedness.

Full-Truthful Implementation in Nash Equilibria

We consider full-truthful Nash implementation, which requires that truth telling by each agent should be a Nash equilibrium of a direct revelation mechanism, and that the set of Nash equilibrium outcomes of the mechanism should coincide with the f -optimal outcome. We show that restricted monotonicity together with an auxiliary condition called boundedness is both necessary and sufficient for full-truthful Nash implementation. We also prove that full-truthful Nash implementation is equivalent to secure implementation (Saijo et al. (2005)). This gives us an alternative characterization of securely implementable social choice functions.

A Characterization of the Randomized Uniform Rule

We consider the problem of allocating several units of an indivisible object among the agents with single-peaked and risk-averse utility functions. We introduce equal probability for the best, and show that the randomized uniform rule is the only randomized rule satisfying strategy-proofness, Pareto optimality, and equal probability for the best. This is an alternative characterization of the result of Ehlers and Klaus (2004).The Randomized Uniform Rule, Single-Peaked Utility Functions, Equal Probability for the Best, Strategy-Proofness, Indivisibility