[vismit2000]

Little Mathematics Library – Elements of Game Theory: https://mirtitles.org/2012/09/06/little-mathematics-library-...

This is a very nice book covering mixed strategy in game theory.

A very nice motivating example from the book: "There are two cards, an ace and a deuce. Player A draws either of the two at random; B does not see which card is drawn. If A has drawn the ace, he says "I've got the ace" and demands a dollar from his opponent. If A has drawn the deuce, then he may either (A1) say "I've got the ace" and demand a dollar from his opponent or (A2) confess that he has got the deuce and pay his opponent a dollar. The opponent, if he is paid the dollar voluntarily, can only accept it. If, however, a dollar is demanded from him, then he may either (B1) believe that player A has got the ace and give him the dollar or (B2) demand a check so as to see whether A's statement is true or not. If it is found that A does have the ace, B must pay A two dollars. If, however, it is found that A is bluffing B and has the deuce, player A pays B two dollars. Analyze the game and find the optimal strategy for each player and the expected payoff."