Agents are substitutes condition

This is known as the agents are substitutes condition (Shapley [65]). A subset of agents together have greater economic value than all of them separately. It is implied by submodularity of V(-). 

In the shortest path case, the agents are substitutes condition is violated. Agents on the same path complement each other, in that no agent on the top path can be selected unless all other agents on the top path are selected. The marginal product of the agents on the top path is less than the sum of their individual marginal products. 

To summarize, when the agents are substitutes condition holds, the VCG auction works without problem. When the agents are substitutes condition is violated, then economic power is in the hands of the bidders, unless, one is prepared to use an auction that does not share some of the properties of the VCG auction. Here we shall argue that the prospects in this regard are bleak. 

Theorem 7.3 (Bikhchandani and Ostroy [12]) The agents are substitutes condition holds if and only if there exists an optimal solution to (DPS), ((Aj)jeiv such that Xj — V N) — V N j) for all j G N, i.e., the dual provides each agent s marginal product. 

For the domain of preferences being considered, verify that the agents are substitutes condition holds. 

The exposure problem is not the only problem that can occur with an ascending auction. Another is the threshold problem (see Bykowsky et al. [7]) which is an instance of the violation of the agents are substitutes condition. 

The nature of the substituents presence in an aromatic substrate has a large effect on which positions are substituted on nitration. The isomeric ratio of products obtained on nitration is also dependent on the nitration conditions, nitrating agent, nitrating medium and its acidity, acid composition and concentration etc., but often to a lesser extent. 

Further situations in which methadone can seem an unsatisfactory substitution agent are towards the other end of the treatment spectrum. In uncomplicated maintenance treatment or for detoxification, the criticisms which are levelled at methadone relate not so much to the subjective effects, but to the aspects of addictiveness, abuse potential and toxicity. The issue of whether methadone is too addictive to be really suitable for detoxification is considered in detail in Chapter 3, and the controversial subject of methadone risks and deaths in Chapter 1. It is in the relatively milder cases of heroin dependence that buprenorphine treatment as an alternative to methadone has risen to great prominence in several countries, although, importantly, the condition definitely does not have to be mild for this medication to be used. Undoubtedly the introduction of buprenorphine is one of... 

We have already established that the carbene carbon is an electrophilic center and, hence, it should be very easily attacked by nucleophiles. In most reactions we believe that the first reaction step probably involves attachment of a nucleophile to the carbene carbon. In some cases, for instance with several phosphines (49) and tertiary amines (50), such addition products are isolable analytically pure under certain conditions (1 in Fig. 3). For the second step there exists the possibility that the nucleophilic agent may substitute a carbon monoxide in the complex with preservation of the carbene ligand (2 in Fig. 3). One can also very formally think of the carbene complex as an ester type of system [X=C(R )OR with X = M(CO)j instead of X = 0], because the oxygen atom as well as the metal atom in the M (CO) 6 residue are each missing 2 electrons for attainment of an inert gas configuration. So, it is not surprising that the... 

In contrast to esterification, etherification is carried out in an alkaline medium and the etherifying agents are alkyl halides. The general reaction is termed aliphatic nucleophilic substitution and, employed under normal conditions, is of the bimolecular type. 

Pyrolysis of arsabarrelenes (see equation 21 for preparation of arsabarrelenes) leads to elimination of acetylene and is a route to producing arsenins which are substituted in the 2- and 3-positions (equation 22) (77TL1283). This reaction can also be effected under much milder conditions using 3,6-di(2 -pyridyl)-l,2,4,5-tetrazine, which acts as an acetylene abstraction agent (78TL2537). 

Under suitable conditions it is possible to isolate the A-substituted hydroxylamines that are formed as intermediates in the reduction of nitro compounds. For this purpose it is essential in the reduction of aromatic nitro compounds to work with neutral or nearly neutral solutions suitable reducing agents are hydrogen and platinum oxide catalysts in glacial acetic acid,82,83 zinc dust in ammonium chloride solution,84 aluminum amalgam,85 and ammonium sulfide.86 Aliphatic nitro compounds may be reduced as their alkali salts (nitronates) by diborane in tetrahydrofuran, then giving A-alkylhydroxyl-amines 87 for instance, A-cyclohexylhydroxylamine is thus obtained from nitrocyclohexane in 53% yield. However, aliphatic nitro compounds are converted into A-alkylhydroxylamines more simply by catalytic hydrogenation in the presence of palladium-barium sulfate unlike aromatic nitro compounds, aliphatic nitro compounds require an acid medium for reduction to hydroxylamines an oxalic acid medium has proved the most suitable. 

The Friedel-Crafts acylation of thiophenes is a much-used reaction and proceeds generally to give good yields under controlled conditions, despite the fact that aluminium chloride reacts with thiophene to generate tars this problem can be avoided by adding catalyst to the thiophene and the acylating agent tin tetrachloride has been used most frequently. Almost exclusive a-substitution is observed, but where both a-positions are substituted, P-substitution occurs easily. 

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