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Given a set of agents qualifying or disqualifying each other, groupidentification is the task of identifying a socially qualified subgroup ofagents. Social qualification depends on the specific rule used to aggregateindividual qualifications. The classical bribery problem in this context askshow many agents need to change their qualifications in order to change theoutcome in a certain way. Complementing previous results showingpolynomial-time solvability or NP-hardness of bribery for various social rulesin the constructive (aiming at making specific agents socially qualified) ordestructive (aiming at making specific agents socially disqualified) setting,we provide a comprehensive picture of the parameterized computationalcomplexity landscape. Conceptually, we also consider a more fine-grainedconcept of bribery cost, where we ask how many single qualifications need to bechanged, nonunit prices for different bribery actions, and a more generalbribery goal that combines the constructive and destructive setting.

Fine-Grained View on Bribery for Group Identification