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<p>For communication situations where the communication possibilities of players are modeled by an undirected graph, we study to what extent Myerson’s graph-restricted game inherits properties from the original transferable utility game. We focus on monotonicity, additivity, superadditivity, convexity, imputation admissibility, balancedness, total balancedness, population monotonic allocation schemes, and exactness. For each of these properties, we characterize all communication graphs that guarantee the inheritance. We present existing results from the literature and we provide new results regarding monotonicity, additivity, imputation admissibility, and exactness.</p>

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Graph-restricted games and their inheritance of properties

  • 期刊论文

  • 发表日期：

    2025年12月18日

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  • Bas Dietzenbacher,
  • Dries Vermeulen

摘要

For communication situations where the communication possibilities of players are modeled by an undirected graph, we study to what extent Myerson’s graph-restricted game inherits properties from the original transferable utility game. We focus on monotonicity, additivity, superadditivity, convexity, imputation admissibility, balancedness, total balancedness, population monotonic allocation schemes, and exactness. For each of these properties, we characterize all communication graphs that guarantee the inheritance. We present existing results from the literature and we provide new results regarding monotonicity, additivity, imputation admissibility, and exactness.