I'm trying to solve this game theory problem:
Player A and B, each take out one or two matches and guess how many matches the opponent has taken. If one of the players guesses correctly, then the loser has to pay him as many rupees as the sum of the number held by both players. Otherwise, the payout is zero. Write down the payoff matrix and obtain the optimal strategies of both players.
I came up with this game matrix. For each strategy (a,b) a is the number of matches taken by the player and b is the player's guess.
$$ \begin{bmatrix} & (1,1) & (1,2) & (2,1) & (2,2)\\ (1,1) & 0 & 2 & -3 & 0\\ (1,2) &-2 & 0 & 0 & 3\\ (2,1) & 3 & 0 & 0 & -4\\ (2,2) & 0 & -3 & 4 & 0\\ \end{bmatrix} $$ The game has no saddle point and there are no dominated rows or columns. I put the matrix in this solver and got the optimal strategies as (0,0,0,0) for each player.
Am I doing something wrong?