Заседание общемосковского семинара
18 ноября на очередном заседании семинара был представлен доклад "New Bounds for Simple Games ", докладчик – Аркадий Слинько (Arkadii Slinko), профессор университета Aukland, New Zealand.
Abstract: Simple game is a mathematical structure that reflects the distribution of power in a group of players and one of the most natural classes of games are weighted majority games. A simple game is roughly weighted if there exists a system of weights and a threshold such that all coalitions whose combined weight is above the threshold are winning and all coalitions hose combined weight is below the threshold are losing and a tie-breaking is needed to classify the coalitions whose combined weight is exactly the threshold. For example, Gabel'man's games that play a significant role in the theory are roughly weighted but not weighted.
Several necessary and sufficient conditions that guarantee weightedness are known. In this paper we give necessary and sufficient conditions for a simple game to have rough weights. We also define two functions that measure the deviation of a simple game with n players from a weighted majority game and roughly weighted majority game, respectively. We derive lower and upper bounds for these functions. We also investigate rough weightedness of simple games with a small number of players.С работами профессора Слинько можно ознакомиться по адресу: http://www.math.auckland.ac.nz/~slinko/