A simplest model for choice of action under uncertainty

A new design of automata («estimating» automata) is proposed; whereby automata of asymptotically optimal sequences function. It is shown that in stationary and switchable media, antagonistic games, allocation games and other classes of games the behaviour of estimating automata is analogous to that of automata with linear tactics and the like. Also, the effectiveness of the behaviour of an estimating automaton is obtained for an arbitrary game with arbitrary players. (In such a game the automaton insures a gain for itself at least equal to the maximal guarnteed one). General laws for collective behaviour of estimating automata and automata of asymptotically optimal sequences are discussed.