  The general picture of game theoretic modeling dealt with here 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. In this Part I approach
players in groups are not independent rational optimizers. They are either
directly controlled by principals and serve the interests of the latter
(pressure and collaboration setting) or they resist the actions of the
principals (pressure and resistance setting) by evolving their strategies in an
'evolutionary manner' via interactions with other players subject to certain
clear rules, deterministic or stochastic. The examples of the real world
problems involved include government representatives (often referred to in the
literature as benevolent dictators) chasing corrupted bureaucrats, inspectors
chasing tax-paying avoidance, police acting against terrorist groups or models
describing the attacks of computer or biological viruses. Other class of
examples concerns appropriate (or better optimal) 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. Such management
can also deal with the processes of merging and splitting of functional units
(say, firms or banks) or the coalition building of agents. The actions of the
big players effectively control the distribution of small players among their
possible strategies and can influence the rules of their interaction.
