You and your friend have come up with the following simple game to pass the time: at each round, you simultaneously call "heads" or "tails". If you have both called the same thing, your friend wins one point; if your calls differ, you win one point. Set up the payoff matrix.
A) $\begin{array} { l }
\quad\quad\quad\quad\text { friend } \
\quad\quad\quad\quad\quad H \quad T \
\mathrm { you} \begin{array} { l }
H \
{ T }
\end{array} \left[ \begin{array} { l l }
-1&1\1&-1
\end{array} \right] \
\end{array}$
B) $\begin{array} { l }
\quad\quad\quad\quad\text { friend } \
\quad\quad\quad\quad\quad H \quad T \
\mathrm { you} \begin{array} { l }
H \
{ T }
\end{array} \left[ \begin{array} { l l }
1&1\-1&-1
\end{array} \right] \
\end{array}$

C) $\begin{array} { l }
\quad\quad\quad\quad\text { friend } \
\quad\quad\quad\quad\quad H \quad T \
\mathrm { you} \begin{array} { l }
H \
{ T }
\end{array} \left[ \begin{array} { l l }
-1&-1\1&1
\end{array} \right] \
\end{array}$

D) $\begin{array} { l }
\quad\quad\quad\quad\text { friend } \
\quad\quad\quad\quad\quad H \quad T \
\mathrm { you} \begin{array} { l }
H \
{ T }
\end{array} \left[ \begin{array} { l l }
1&-1\-1&1
\end{array} \right] \
\end{array}$

E) $\begin{array} { l }
\quad\quad\quad\quad\text { friend } \
\quad\quad\quad\quad\quad H \quad T \
\mathrm { you} \begin{array} { l }
H \
{ T }
\end{array} \left[ \begin{array} { l l }
2&-1\-1&2
\end{array} \right] \
\end{array}$

Question

You and your friend have come up with the following simple game to pass the time: at each round, you simultaneously call "heads" or "tails". If you have both called the same thing, your friend wins one point; if your calls differ, you win one point. Set up the payoff matrix.  
A) $\begin{array} { l } 
\quad\quad\quad\quad\text { friend } \
\quad\quad\quad\quad\quad H \quad T  \
\mathrm { you} \begin{array} { l } 
H \
 { T }
\end{array} \left[ \begin{array} { l l } 
-1&1\1&-1
\end{array} \right] \
\end{array}$  
B)   $\begin{array} { l } 
\quad\quad\quad\quad\text { friend } \
\quad\quad\quad\quad\quad H \quad T  \
\mathrm { you} \begin{array} { l } 
H \
 { T }
\end{array} \left[ \begin{array} { l l } 
1&1\-1&-1
\end{array} \right] \
\end{array}$
 
C)   $\begin{array} { l } 
\quad\quad\quad\quad\text { friend } \
\quad\quad\quad\quad\quad H \quad T  \
\mathrm { you} \begin{array} { l } 
H \
 { T }
\end{array} \left[ \begin{array} { l l } 
-1&-1\1&1
\end{array} \right] \
\end{array}$
 
D)   $\begin{array} { l } 
\quad\quad\quad\quad\text { friend } \
\quad\quad\quad\quad\quad H \quad T  \
\mathrm { you} \begin{array} { l } 
H \
 { T }
\end{array} \left[ \begin{array} { l l } 
1&-1\-1&1
\end{array} \right] \
\end{array}$
 
E)    $\begin{array} { l } 
\quad\quad\quad\quad\text { friend } \
\quad\quad\quad\quad\quad H \quad T  \
\mathrm { you} \begin{array} { l } 
H \
 { T }
\end{array} \left[ \begin{array} { l l } 
2&-1\-1&2
\end{array} \right] \
\end{array}$

Quizplus · Accepted Answer

The payoff matrix should be set up so that the player who wins the round gets a positive payoff and the player who loses the round gets a negative payoff. In this case, the friend wins if they both call the same thing, so the payoff for the friend is 1 in that case. If they call different things, you win, so the payoff for you is 1 in that case. The payoff matrix should therefore be:$\begin{array} { l } \quad\quad\quad\quad\text { friend } \\quad\quad\quad\quad\quad H \quad T  \\mathrm { you} \begin{array} { l } H \ { T }\end{array} \left[ \begin{array} { l l } -1&1\1&-1\end{array} \right] \\end{array}$

You and Your Friend Have Come Up with the Following