Equilibrium in safe strategies

The interaction of many participants dividing among themselves a resource located on a certain set is investigated. For the problem stated, the Mash equilibrium does not exist in most of the cases, but at the same time there is an intuitively perceived stable rational behavior of participants, which relies on the reflexive accounting of mutual threats. For the description of such a behavior, the definition is set up of an equilibrium in safe strategies (ESS's), which coincides with the strict Nash equilibrium where it is available and exists for those situations in the stated problem where it is unavailable. Using the introduced definition, the initial problem is examined. The introduced equilibrium is also illustrated by examples of bimatrix games, a competitive system of stimulation, and a game in which the ESS's does not exist.