Coalitional Manipulations and Immunity of the Shapley Value

We consider manipulations in the context of coalitional games, where a coalition aims to increase the total payoff of its members. An allocation rule is immune to coalitional manipulation if no coalition can benefit from internal reallocation of worth on the level of its subcoalitions (reallocation-proofness), and if no coalition benefits from a lower worth while all else remains the same (weak coalitional monotonicity). Replacing additivity in Shapley's original characterization by these requirements yields a new foundation of the Shapley value, i.e., it is the unique efficient and symmetric allocation rule that awards nothing to a null player and is immune to coalitional manipulations. We further find that for efficient allocation rules, reallocation-proofness is equivalent to constrained marginality, a weaker variant of Young's marginality axiom. Our second characterization improves upon Young's characterization by weakening the independence requirement intrinsic to marginality

Efficient extensions of communication values

We study values for transferable utility games enriched by a communication graph. The most well-known such values are component-efficient and characterized by some link-deletion property. We study efficient extensions of such values: for a given component-efficient value, we look for a value that (i) satisfies efficiency, (ii) satisfies the link-deletion property underlying the original component-efficient value, and (iii) coincides with the original component-efficient value whenever the underlying graph is connected. Béal et al. (2015) prove that the Myerson value (Myerson, 1977) admits a unique efficient extension, which has been introduced by van den Brink et al. (2012). We pursue this line of research by showing that the average tree solution (Herings et al., 2008) and the compensation solution (Béal et al., 2012a) admit similar unique efficient extensions, and that there exists no efficient extension of the position Value (Meessen, 1988; Borm et al., 1992). As byproducts, we obtain new characterizations of the average tree solution and the compensation solution, and of their efficient extensions

Efficient extension of the Myerson value

We study values for transferable utility games enriched by a communication graph (CO-games) where the graph does not necessarily affect the productivity but can influence the way the players distribute the worth generated by the grand coalition. Thus, we can envisage values that are efficient instead of values that are component efficient. For CO-games with connected graphs, efficiency and component efficiency coincide. In particular, the Myerson value (Myerson, 1977) is efficient for such games. Moreover, fairness is characteristic of the Myerson value. We identify the value that is efficient for all CO-games, coincides with the Myerson value for CO-games with connected graphs, and satisfies fairness

AMNIOTE PHYLOGENY AND THE IMPORTANCE OF FOSSILS

Several prominent cladists have questioned the importance of fossils in phylogenctic inference, and it is becoming increasingly popular to simply fit extinct forms, if they are considered at all, to a cladogram of Recent taxa. Gardiner's (1982) and LØvtrup's (1985) study of amniote phylogeny exemplifies this differential treatment, and we focused on that group of organisms to test the proposition that fossils cannot overturn a theory of relationships based only on the Recent biota. Our parsimony analysis of amniote phylogeny, special knowledge contributed by fossils being scrupulously avoided, led to the following best fitting classification, which is similar to the novel hypothesis Gardiner published: (lepidosaurs (turtles (mammals (birds, crocodiles)))). However, adding fossils resulted in a markedly different most parsimonious cladogram of the extant taxa: (mammals (turtles (lepidosaurs (birds, crocodiles)))). That classification is like the traditional hypothesis, and it provides a better fit to the stratigraphic record. To isolate the extinct taxa responsible for the latter classification, the data were successively partitioned with each phylogenetic analysis, and we concluded that: (1) the ingroup, not the outgroup, fossils were important; (2) synapsid, not reptile, fossils were pivotal; (3) certain synapsid fossils, not the earliest or latest, were responsible. The critical nature of the synapsid fossils seemed to lie in the particular combination of primitive and derived character slates they exhibited. Classifying those fossils, along with mammals, as the sister group to the lineage consisting of birds and crocodiles resulted in a relatively poor fit to data; one involving a 2—4 fold increase in evolutionary reversals! Thus, the importance of the critical fossils, collectively or individually, seems to reside in their relative primitive-ness, and the simplest explanation for their more conservative nature is that they have had less time to evolve. While fossils may be important in phylogenetic inference only under certain conditions, there is no compelling reason to prejudge their contribution. We urge systematists to evaluate fairly all of the available evidence.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73857/1/j.1096-0031.1988.tb00514.x.pd

Solidarity within a Fixed Community

CNRS : 3; AERES : BInternational audienceWe study the consequences of a solidarity property that specifies how a value for cooperative games should respond if some player forfeits his productivity, i.e., becomes a null player. Nullified solidarity states that in this case either all players weakly gain together or all players weakly lose together. Combined with efficiency, the null game property, and a weak fairness property, we obtain a new characterization of the equal division value

Characterizations of Weighted and Equal Division Values

CNRS 2 ; AERES AInternational audienc