  As part of a generalized "prisoners' dilemma", is considered that the
evolution of a population with a full set of behavioral strategies limited only
by the depth of memory. Each subsequent generation of the population
successively loses the most disadvantageous strategies of behavior of the
previous generation. It is shown that an increase in memory in a population is
evolutionarily beneficial. The winners of evolutionary selection invariably
refer to agents with maximum memory. The concept of strategy complexity is
introduced. It is shown that strategies that win in natural selection have
maximum or near maximum complexity. Despite the fact that at a separate stage
of evolution, according to the payout matrix, the individual gain, while
refusing to cooperate, exceeded the gain obtained while cooperating. The
winning strategies always belonged to the so-called respectable strategies that
are clearly prone to cooperation.
