Coalition formation in simple games with dominant players

A player, in a proper and monotonic simple game, is dominant if he holds a “strict majority” within a winning coalition. A (non-dictatorial) simple game is dominated if it contains exactly one dominant player. We investigate several possibilities of coalition formation in dominated simple games, under the assumption that the dominant player is given a mandate to form a coalition. The relationship between the various hypotheses on coalition formation in dominated games is investigated in the first seven sections. In the last section we classify real-life data on European parliaments and town councils in Israel.