Solution
Solve the Matrix
Show the problem again
In a zero-sum game, the row player's payoff matrix is [[3, −1], [−2, 4]]. Both players play their optimal mixed strategies. What is the value of the game to the row player?
Worked solution
The value is 1 per play to the row player, with Row playing (3/5, 2/5) and Column playing (1/2, 1/2). With no saddle point, both players mix to make the opponent indifferent. Row plays the first row with probability p where 3p − 2(1 − p) = −p + 4(1 − p), giving p = 3/5. Column plays the first column with probability q where 3q − (1 − q) = −2q + 4(1 − q), giving q = 1/2. Plugging in, the game's value is 3(3/5) − 2(2/5) = 1.
Source: Standard two-player zero-sum matrix game from the game-theory literature. Statement written for AxiomIQ.