Dominated by a Mixture

Row chooses a row and Column chooses a column, simultaneously and once. Row's payoffs: Row 1: 3, 3, 4 Row 2: 4, 1, 2 Row 3: 3, 2, 0 Column's payoffs: Row 1: 4, 2, 1 Row 2: 3, 0, 1 Row 3: 0, 2, 4 (The entry in position (i, j) is that player's payoff when Row plays i and Column plays j.) Rational players repeatedly delete every strategy that is strictly dominated by some pure or mixed strategy among those remaining. No pure strategy is strictly dominated by another pure strategy at the start. Exactly one outcome survives the full process. What is the product of the two players' payoffs at that outcome? Give an integer.

• combinations
• dominant strategy
• nash equilibrium

Source: Dominance by mixed strategies is standard textbook material (e.g. Osborne and Rubinstein); numbers original to AxiomIQ.