Three-Stage Entry Game: the Strategic Effects of Advertising
Top responsiveness was shown by Alcalde and Revilla [AR] to guarantee the existence of core stable partitions in hedonic coalition formation games. In this paper we prove the existence of Nash stable partitions under top responsiveness when a mutuality condition is imposed.
There exist several possibilities of fuzzification of a coalitional game. It is quite usual to fuzzify, e. g., the concept of coalition, as it was done in [1]. Another possibility is to fuzzify the expected pay-offs, see [3, 4]. The latter possibility is dealt even here. We suppose that the coalitional and individual pay-offs are expected only vaguely and this uncertainty on the input'' of the game rules is reflected also by an uncertainty of the derived output'' concept like superadditivity, core,...
Given a graph H and an integer r ≥ 2, let G → (H,r) denote the Ramsey property of a graph G, that is, every r-coloring of the edges of G results in a monochromatic copy of H. Further, let and define the Ramsey density as the infimum of m(G) over all graphs G such that G → (H,r). In the first part of this paper we show that when H is a complete graph Kₖ on k vertices, then , where R = R(k;r) is the classical Ramsey number. As a corollary we derive a new proof of the result credited to Chvatál...