The Complexity of Manipulation of k-Coalitional Games on Graphs
This addresses manipulation issues in coalition formation for organizers who rely on agent-reported data, but it is incremental as it extends complexity analysis to a specific game setting.
The paper tackles the problem of agents falsely reporting friendships to manipulate coalition formation in k-coalitional games on graphs, and it analyzes the computational complexity of finding such manipulations, including a new socially-aware type, with simulation results on frequency and algorithm runtimes.
In many settings, there is an organizer who would like to divide a set of agents into $k$ coalitions, and cares about the friendships within each coalition. Specifically, the organizer might want to maximize utilitarian social welfare, maximize egalitarian social welfare, or simply guarantee that every agent will have at least one friend within his coalition. However, in many situations, the organizer is not familiar with the friendship connections, and he needs to obtain them from the agents. In this setting, a manipulative agent may falsely report friendship connections in order to increase his utility. In this paper, we analyze the complexity of finding manipulation in such $k$-coalitional games on graphs. We also introduce a new type of manipulation, socially-aware manipulation, in which the manipulator would like to increase his utility without decreasing the social welfare. We then study the complexity of finding socially-aware manipulation in our setting. Finally, we examine the frequency of socially-aware manipulation and the running time of our algorithms via simulation results.