Noninferior Nash Strategies for Multi-Team Systems

This paper is concerned with the optimization of systems that are controlled by several teams of decision makers. The decision makers within each team cooperate for the benefit of their team. On the other hand, the teams compete among themselves in order to achieve an objective that relates to the overall performance of the system. An approach that merges concepts from team theory and game theory for dealing with such systems and a solution called the noninferior Nash strategy are introduced. This multi-team solution provides a new framework for analyzing hierarchically controlled systems so as to address complicated coordination problems among the decision makers. The properties of the noninferior Nash solution in static multi-team systems are investigated and necessary conditions for its existence are derived. Analytical expressions for the noninferior Nash strategies are derived for a class of linear-quadratic static multi-team games. In order to deal with the issue of nonuniqueness of the solution, the concept of a noninferior Nash strategy with a team leader is introduced. Several examples are presented to illustrate the results.     

Tris(arylmethyl) derivatives of 1,3,5-trimethoxy- and 1,3,5-triethylbenzene

The hexasubstituted benzenes 7 and 9b were synthesized starting from 3 and 8b, respectively. In the crystal, 9b adopts the fully alternated conformation with all arylmethyl groups oriented syn.     

Modulable and Highly Diastereoselective Carbometalations of Cyclopropenes

The copper‐catalyzed carbomagnesiation reaction of cyclopropenyl esters 1 leads to various substituted cyclopropanes species 3 in good yields with very high diastereoselectivities. The reaction proceeds through a syn‐chelated carbomagnesiation reaction and could be extended to various cyclopropenylmethyl ester derivatives 5 . The potential of this approach was illustrated by the preparation of two consecutive all‐carbon quaternary stereocenters. However, the carbometalation reaction needs to be performed at temperature ranging from ?35 to ?20 °C to avoid subsequent fragmentation reaction into stereodefined β,γ‐nonconjugated unsaturated esters 4 . Alternatively, the carbocupration reaction with organocopper species could also be performed to leads to configurationally stable cyclopropyl copper species 2[Cu] . Additionally, when the Lewis acid character of the copper center is decreased (i.e., RCuCNLi), the reaction proceed with an anti‐selectivity. The diastereodivergent behavior of these organometallic species is of synthetic interest, since both diastereomers syn‐ 3 and anti‐ 3 can be obtained, at will, from the same precursor cyclopropenyl esters 1 .     

Computational Insights of Selective Intramolecular O-atom Transfer Mediated by Bioinspired Copper Complexes

The stereoselective copper-mediated hydroxylation of intramolecular C−H bonds from tridentate ligands is reinvestigated using DFT calculations. The computational study aims at deciphering the mechanism of C−H hydroxylation obtained after reaction of Cu(I) precursors with dioxygen, using ligands bearing either activated ( L¹ ) or non-activated ( L² ) C−H bonds. Configurational analysis allows rationalization of the experimentally observed regio- and stereoselectivity. The computed mechanism involves the formation of a side-on peroxide species ( P ) in equilibrium with the key intermediate bis-(μ-oxo) isomer ( O ) responsible for the C−H activation step. The P/O equilibrium yields the same activation barrier for the two complexes. However, the main difference between the two model complexes is observed during the C−H activation step, where the complex bearing the non-activated C−H bonds yields a higher energy barrier, accounting for the experimental lack of reactivity of this complex under those conditions.     

On the Stackelberg strategy in nonzero-sum games

The properties of the Stackelberg solution in static and dynamic nonzero-sum two-player games are investigated, and necessary and sufficient conditions for its existence are derived. Several game problems, such as games where one of the two players does not know the other's performance criterion or games with different speeds in computing the strategies, are best modeled and solved within this solution concept. In the case of dynamic games, linear-quadratic problems are formulated and solved in a Hilbert space setting. As a special case, nonzero-sum linear-quadratic differential games are treated in detail, and the open-loop Stackelberg solution is obtained in terms of Riccati-like matrix differential equations. The results are applied to a simple nonzero-sum pursuit-evasion problem.This work was supported in part by the US Air Force under Grant No. AFOSR-68-1579D, in part by NSF under Grant No. GK-36276, and in part by the Joint Services Electronics Program under Contract No. DAAB-07-72-C-0259 with the Coordinated Science Laboratory, University of Illinois, Urbana, Illinois.     

A conformationally flexible tetrahydroxycalix[4]arene adopting the unusual 1,3-alternate conformation

The use of a chiral solvating agent enabled the determination of the NMR-silent ring-inversion process of the ketocalixarene 3. Spectroscopic and crystal data indicate that 3 adopts the unusual 1,3-alternate conformation.