Independent set games are cooperative games defined on graphs, where players are edges and the value of a coalition is the maximum cardinality of independent sets in the subgraph defined by the coalition. In this paper, we investigate the convexity of independent set games, as convex games possess many nice properties both economically and computationally. For independent set games introduced by Deng et al. (Math. Oper. Res., 24:751-766, 1999), we provide a necessary and sufficient characterization for the convexity, i.e., every non-pendant edge is incident to a pendant edge in the underlying graph. Our characterization immediately yields a polynomial time algorithm for recognizing convex instances of independent set games. Besides, we introduce a new class of independent set games and provide an efficient characterization for the convexity.

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关于独立集博弈的凸性

独立集博弈是在图上定义的合作博弈，其中玩家是边，联盟的值是联盟定义的子图中独立集的最大基数。在本文中，我们研究了独立集博弈的凸性，因为凸博弈在经济和计算上都具有许多不错的特性。对于 Deng 等人介绍的独立游戏。(Math. Oper. Res., 24:751-766, 1999)，我们为凸性提供了必要且充分的表征，即每个非悬垂边都与底层图中的悬垂边相关。我们的表征立即产生了一个多项式时间算法，用于识别独立集游戏的凸实例。此外，我们引入了一类新的独立集博弈，并为凸性提供了有效的表征。