I am absolutely new to decision theory . I came across this following payoff matrix in the book.(Math. Stats : John E Freund).
Player A I II Player B 1 7 -4 2 8 10
The value of the game is given as 8 units.However i . have a question . I agree the optimal strategy for Play B is "2" . But i want to argue that the optimal choice for player A is 2 . This is because in decision theory the assumption is made that "each player must choose a strategy without knowing what the opponent is going to do and that once a player has made a choice it can not be changed" ..Going by this logic, the optimal strategy for player A should be II , because i see in that case , the loss would be less overall for the moves of player B . This , logic if true gives the value of the game to be 10 , which is not correct. I want to know , where i am wrong.