Decide whether the game is strictly determined. If it is, give the players' optimal pure strategies and the value of the game.
$\begin{array} { l }
\quad\quad\quad\quad\text { B } \
\quad\quad\quad\quad p \quad q\quad r \
\mathrm { A } \begin{array} { l }
a \
{ b }
\end{array} \left[ \begin{array} { l l }
-3&2&-4\-3&3&-3
\end{array} \right] \
\end{array}$
A)A's optimal strategy is a; B's optimal strategy is q; value: 1
B) A's optimal strategy is b; B's optimal strategy is q; value: 1
C) A's optimal strategy is b; B's optimal strategy is p; value: 1
D) A's optimal strategy is a; B's optimal strategy is p; value: 1.5
E) The game is not strictly determined

Question

Decide whether the game is strictly determined. If it is, give the players' optimal pure strategies and the value of the game.   
$\begin{array} { l } 
\quad\quad\quad\quad\text { B } \
\quad\quad\quad\quad p \quad q\quad r  \
\mathrm { A } \begin{array} { l } 
a \
 { b }
\end{array} \left[ \begin{array} { l l } 
-3&2&-4\-3&3&-3
\end{array} \right] \
\end{array}$  
A)A's optimal strategy is a; B's optimal strategy is q; value: 1
B) A's optimal strategy is b; B's optimal strategy is q; value: 1 
C) A's optimal strategy is b; B's optimal strategy is p; value: 1
D) A's optimal strategy is a; B's optimal strategy is p; value: 1.5
E) The game is not strictly determined

Quizplus · Accepted Answer

The game is not strictly determined because there is no single pair of strategies that guarantees each player their maximum payoff regardless of the opponent's action. For player A, choosing between rows a and b does not provide a consistently higher payoff across all of B's strategies. Similarly, for player B, choosing between columns p, q, and r does not guarantee a consistently lower payoff to A. The payoffs vary depending on the combination of strategies chosen, indicating that there is no strictly dominant strategy for either player.

Decide Whether the Game Is Strictly Determined A)A's Optimal Strategy Is A; B's Optimal Strategy Is Q;