Forward-looking Pairwise Stability in Networks with Externalities

We consider cooperation situations where players have network relations. Networks evolve according to a stationary transition probability matrix and at each moment in time players receive payoffs from a stationary allocation rule. Players discount the future by a common factor. The pair formed by an allocation rule and a transition probability matrix is called a forward-looking network formation scheme if, first, the probability that a link is created is positive if the discounted, expected gains to its two participants are positive, and if, second, the probability that a link is eliminated is positive if the discounted, expected gains to at least one of its two participants are positive. The main result is the existence, for all discount factors and all value functions, of a forward-looking network formation scheme. Furthermore, we can always nd a forward-looking network formation scheme such that (i) the allocation rule is component balanced and (ii) the transition probabilities increase in the di erence in payo s for the corresponding players responsible for the transition. We use this dynamic solution concept to explore the tension between e ciency and stability.

Beta-Hydroxyimino Phosphorus Derivatives. An Efficient Tool in Organic Synthesis

[EN] The purpose of this review article is to illustrate synthetic aspects of functionalized phosphorus derivatives containing an oximo moiety at the beta-position. First section will be focused on the synthesis of phosphine oxides, phosphonates or phosphonium salts containing an oxime group. The synthesis of these derivatives comprises the carbon–phosphorus single bond construction by reaction of haloximes with phosphorus derivatives, nucleophilic addition of phosphorus reagents to carbonyl compounds, or nucleophilic addition of phosphorus reagents to nitro olefins. This section will also concentrate on the most practical routes for the synthesis of the target compounds, through carbon–nitrogen double bond formation, which are as follows: condensation processes of carbonyl compounds and hydroxylamine derivatives or addition of hydroxylamines to allenes or alkynes. The preparative use of beta-oximo phosphorus derivatives as synthetic intermediates will be discussed in a second section, comprising olefination reaction, oxidation of oximes to nitrile oxides by reaction at the C-N double bond of the oxime moiety, oxidation of these substrates to nitrosoalkenes, reduction to the corresponding hydroxylamines and some reactions at the hydroxyl group of the hydroxyimino moiety.

Efficiency vs. Stability in a Mixed Network Formation Model

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