The general picture of modeling dealt with in this talk is characterized by a set of big players, also referred to as principals or major agents, acting on the background of large pools of small players, the impact of the behavior of each small player in a group on the overall evolution decreasing with the increase of the size of the group. The examples of the real world problems involved include government representatives chasing corrupted bureaucrats, inspectors chasing tax-paying avoidance, police acting against terrorist groups or models describing the attacks of computer or biological viruses. This includes the problem of optimal allocation of the budget of big players, appropriate management of complex stochastic systems consisting of large number of interacting components (agents, mechanisms, vehicles, subsidiaries, species, police units, robot swarms, etc), which may have competitive or common interests, the processes of merging and splitting of functional units (say, firms or banks) or the coalition building of agents.

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