Signal decoding with help of finite automata: application to games with incomplete information

Matrix games with incomplete information on both sides and public signal on the state of game represented by random binary code of fixed length are considered. Players are computationally bounded and are only able to play strategies to finite automata of different sizes: $m$ for Player 1 and $n$ for Player 2 where $m\gg n$. We obtain a lower bound for $m$ and an upper bound for $n$ which may turn the original game with incomplete information for both players into a game with incomplete information for Player 2.