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Top responsiveness and Nash stability in coalition formation games

Dinko Dimitrov, Shao Chin Sung (2006)

Kybernetika

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.

Two approaches to fuzzification of payments in NTU coalitional game.

Milan Mares (2002)

Mathware and Soft Computing

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,...

Two variants of the size Ramsey number

Andrzej Kurek, Andrzej Ruciński (2005)

Discussiones Mathematicae Graph Theory

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 m ( G ) = m a x F G | E ( F ) | / | V ( F ) | and define the Ramsey density m i n f ( H , r ) 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 m i n f ( H , r ) = ( R - 1 ) / 2 , where R = R(k;r) is the classical Ramsey number. As a corollary we derive a new proof of the result credited to Chvatál...

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