Existence theorems of the \(\omega\)-limit states for conflict dynamical systems. (English) Zbl 1324.37039

The paper continues the series of publications by the authors on dynamical systems describing conflict phenomena; see, for example, [the author, Math. Methods Oper. Res. 59, No. 2, 303- 313 (2004; Zbl 1106.91015); Ukr. Math. J. 63, No. 2, 222–235 (2011; Zbl 1264.81204)]. Here the author considers transformations of pairs of probability measures \((\mu_N,\nu_N)\), and for some iterative procedures, studies the limit behavior, as \(N\to \infty\), of trajectories including the existence of limit states.


37N40 Dynamical systems in optimization and economics
91A15 Stochastic games, stochastic differential games