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We consider a setting where one has to organize one or several group activities for a set of agents. Each agent will participate in at most one activity, and her preferences over activities depend on the number of participants in the activity. The goal is to assign agents to activities based on their preferences. We put forward a general model for this setting, which is a natural generalization of anonymous hedonic games. We then focus on a special case of our model, where agents' preferences are binary, i.e., each agent classifies all pairs of the form "(activity, group size)" into ones that are acceptable and ones that are not. We formulate several solution concepts for this scenario, and study them from the computational point of view, providing hardness results for the general case as well as efficient algorithms for settings where agents' preferences satisfy certain natural constraints.

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a b s t r a c tWe study a resource allocation problem where jobs have the following characteristic: each job consumes some quantity of a bounded resource during a certain time interval and induces a given profit. We aim to select a subset of jobs with maximal total profit such that the total resource consumed at any point in time remains bounded by the given resource capacity.While this case is trivially N P -hard in general and polynomially solvable for uniform resource consumptions, our main result shows the N P -hardness for the case of general resource consumptions but uniform profit values, i.e. for the case of maximizing the number of performed jobs. This result applies even for proper time intervals.We also give a deterministic (1/2−ε)-approximation algorithm for the general problem on proper intervals improving upon the currently known 1/3 ratio for general intervals. Finally, we study the worst-case performance ratio of a simple greedy algorithm.

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