In a hedonic diversity game (HDG) there are two types of agents (red and blue agents) that need to form disjoint coalitions, i.e., subgroups of agents. Each agent’s preferences over the coalitions depend on the relative number of agents of the same type in her coalition. In the special case of a dichotomous hedonic diversity game (DHDG) each agent distinguishes between approved and disapproved fractions only. We aim at outcomes that are stable against agents’ deviations, and at outcomes that maximize social welfare. In particular, we show that the strict core of a DHDG may be empty even in instances with only three agents, while each HDG with two agents has a non-empty strict core. We also provide several computational complexity results for DHDGs with respect to the number of fractions approved per agent. For instance, we prove that deciding whether a DHDG has a non-empty strict core is \(\textsf {NP}\)-complete even when each agent approves of at most three fractions. In addition, we show that deciding whether a DHDG admits a Nash stable outcome is \(\textsf {NP}\)-complete even in restricted settings with only two approved fractions per agent—therewith, improving a result in the literature. For the task of maximizing social welfare, we apply approval scores and Borda scores from voting theory. For DHDGs and approval scores, we draw the sharp separation line between polynomially solvable and \(\textsf {NP}\)-complete cases with respect to the fixed number of approved fractions per agent. We complement these findings with an \(\textsf {NP}\)-completeness result for HDGs under Borda scores.

在享乐多样性游戏（HDG）中，有两种类型的智能体（红色和蓝色智能体）需要形成不相交的联盟，即智能体子组。每个智能体对联盟的偏好取决于其联盟中相同类型智能体的相对数量。在二分享乐多样性游戏（DHDG）的特殊情况下，每个代理仅区分批准和不批准的分数。我们的目标是针对代理人偏差保持稳定的结果，以及最大化社会福利的结果。特别是，我们表明，即使在只有三个代理的实例中，DHDG 的严格核心也可能是空的，而每个具有两个代理的 HDG 都有一个非空的严格核心。我们还提供了 DHDG 的几个计算复杂性结果，涉及每个代理批准的分数数量。例如，\(\textsf {NP}\) -即使每个代理最多批准三个分数也是完整的。此外，我们表明，决定 DHDG 是否承认纳什稳定结果是\(\textsf {NP}\)完成的，即使在每个代理只有两个批准分数的限制环境中也是如此，从而改善了文献中的结果。对于社会福利最大化的任务，我们应用投票理论中的支持分数和博达分数。对于 DHDG 和批准分数，我们在多项式可解和\(\textsf {NP}\)完整案例之间就每个代理批准分数的固定数量划出了清晰的分界线。我们用 Borda 分数下 HDG 的\(\textsf {NP}\)完整性结果来补充这些发现。