| Two important problems in cooperative games are the coalition formation of players and the allocation schemes of profits among the players (so-called solutions of the games). The random order values, which include the Shapley value as a special case, are fundamental point-valued solutions in transferable utility games (TU-games). We prove the population monotonicity, i.e., the monotonicity of allocated individual values with respect to coalitions, of the random order values in convex games. We also discuss coalition formation in TU-games as hedonic games based on the random order values. We prove that the coalition structure obtained from the top coalition algorithm satisfies some stability properties in hedonic games. |
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