  Many decision problems in economics, information technology, and industry can
be transformed to an optimal stopping of adapted random vectors with some
utility function over the set of Markov times with respect to filtration build
by the decision maker's knowledge. The optimal stopping problem formulation is
to find a stopping time which maximizes the expected value of the accepted
(stopped) random vector's utility.
  There are natural extensions of optimal stopping problem to stopping the
games-the problem of stopping random vectors by two or more decision makers.
Various approaches dependent on the information scheme and the aims of the
agents in a considered model. This report unifies a group of non-cooperative
stopping game models with forced cooperation by the role of the agents, their
aims and aspirations (v. Assaf & Samuel-Cahn(1998), Szajowski & Yasuda(1995))
or extensions of the strategy sets (v. Ramsey & Szajowski(2008)).
