Reshef, Moshe and Sam
(based on discussions with Reshef Meir, Moshe Tennenholtz, and Sam Payne)
Tic Tac Toe is played since anciant times. For the common version, where the two players X and O take turns in marking the empty squares in a 3 by 3 board - each player has a strategy that can guarantee a draw. Now suppose that the X player has a budget of Y dollars, the O playare has a budget of 100 dollars and before each round the two players bid who makes the next move.