Method for asymptotic investigation of games between automata

The paper proposes a new method whereby collective behaviour of automata of asymptoticaly optimal sequences [1,2] can be reduced to studying auxiliary Markov chains with a number of states equal to that of sets in the game. Results are formulated that use description of a game in terms of a directed graph. The “slowness hypothesis” and solution of appointment games and games with a common cashier are disproved.