About effective versions of game theoretical semantics for first-order logic

In the article we compare two approaches to effectivisation of game theoretical semantics for first-order logic. One of the approaches was provided by Sergey P. Odintsov, Stanislav O. Speranski, Igor Yu. Shevchenko in the previous article, and it is based on a game-theoretical reconstruction of strategy conception. In this article we provide the other approach — we consider a strategy as a function determined on a set of histories and then we set an equivalence between these two approaches.