A problem of axiomatic construction of a social ranking is studied for the case when individual opinions are given as three-graded rankings. It is shown that the only rule satisfying the axioms introduced is the threshold rule.
In the bilateral assignment problem, source a holds the amount ra of resource of type a, while sink i must receive the total amount xi of the various resources. We look for assignment rules meeting the powerful separability property known as Consistency: “every subassignment of a fair assignment is fair”. They are essentially those rules selecting the feasible flow minimizing the sum ∑i,aW(yia), where W is smooth and strictly convex.
This paper seeks answers to two questions. First, if a greater social activity of an individual enhances oblique (i.e. to non-relatives) transmission of her cultural traits at the expense of vertical (i.e. to children) transmission as well as family size, which behavior is optimal from cultural evolution standpoint? I formalize a general model that characterizes evolutionarily stable social activity. The proposed model replicates the theory of Newson et al. (2007) that fertility decline is caused by increasing role of oblique cultural transmission. Second, if social activity is a rational choice rather than a culturally inherited trait, and if cultural transmission acts on preferences rather than behaviors, which preferences survive the process of cultural evolution? I arrive at a very simple yet powerful result: under mild assumptions on model structure, only preferences which emphasize exclusively the concern for social prestige, i.e. extent to which one’s cultural trait has been picked up by others, survive.
A game with restricted cooperation is a triple (N,v,Ω), where N is a finite set of players, Ω⊂2N is a nonempty collection of feasible coalitions such that N∈Ω, andv:Ω→R is a characteristic function. The definition implies that if Ω=2N, then the game(N,v,Ω)=(N,v) is the classical transferable utility (TU) cooperative game.
The class of all games with restricted cooperation Gr with an arbitrary universal set of players is considered. The prenucleolus and the prekernel for games with restricted cooperation are defined in the same way as the prenucleolus and the prekernel for classical TU games. Necessary and sufficient conditions for the collection Ω to imply the single-valuedness of the prenucleolus are obtained. Axiomatic characterizations of the prenucleolus and of the prekernel for the class with a balanced collection of feasible coalitions Ω are given.
In the collection Ω there may be identical players belonging to the same coalitions. In that case, the set of symmetric preimputations is defined as those where identical players have equal payoffs. The symmetric prenucleolus, being the nucleolus w.r.t. the set of symmetrical preimputations, is defined and characterized.