  In the Group Identification problem, we are given a set of individuals and
are asked to identify a socially qualified subset among them. Each individual
in the set has an opinion about who should be considered socially qualified.
There are several different rules that can be used to determine the socially
qualified subset based on these mutual opinions. In a manipulative attack, an
outsider attempts to exploit the way the used rule works, with the goal of
changing the outcome of the selection process to their liking.
  In recent years, the complexity of group control and bribery based
manipulative attacks in Group Identification has been the subject of intense
research. However, the picture is far from complete, and there remain many open
questions related to what exactly makes certain problems hard, or certain rules
immune to some attacks.
  Supplementing previous results, we examine the complexity of group
microbribery on so-called protective problem instances; that is, instances
where all individuals from the constructive target set are already socially
qualified initially. In addition, we study a relaxed variant of group control
by deleting individuals for the consent rules, the consensus-start-respecting
rule, and the liberal-start-respecting rule. Based on existing literature, we
also formalize three new social rules of the iterative consensus type, and we
provide a comprehensive complexity-theoretic analysis of group control and
bribery problems for these rules.
