Question

In the following incomplete information game, player 1 (P1) selects between U and D, and player 2 (P2) selects between L and R. Player 1 knows which game is being played, player 2 doesn't. The probability that they are playing the game on the left bimatrix is $p = \frac{1}{2}$, and this is common knowledge. \begin{tabular}{cc|c|c|} & & \multicolumn{2}{c}{P2} \\ cline{3-4} & & L & R \\ cline{2-4} \multirow{2}{}{P1} & U & 15,18 & 6,7 \\ cline{2-4} & D & 8,0 & 8,11 \\ cline{2-4} \end{tabular} \begin{tabular}{cc|c|c|} & & \multicolumn{2}{c}{P2} \\ cline{3-4} & & L & R \\ cline{2-4} \multirow{2}{}{P1} & U & 4,18 & 6,7 \\ cline{2-4} & D & 8,0 & 8,11 \\ cline{2-4} \end{tabular} a) Construct the Bayesian normal-form representation of the game. b) Find all Bayesian Nash equilibria of this game.

          In the following incomplete information game, player 1 (P1) selects between U and D, and player 2 (P2) selects between L and R. Player 1 knows which game is being played, player 2 doesn't. The probability that they are playing the game on the left bimatrix is $p = \frac{1}{2}$, and this is common knowledge.

\begin{tabular}{cc|c|c|}
 &  & \multicolumn{2}{c}{P2} \\
cline{3-4}
 &  & L & R \\
cline{2-4}
\multirow{2}{*}{P1} & U & 15,18 & 6,7 \\
cline{2-4}
 & D & 8,0 & 8,11 \\
cline{2-4}
\end{tabular}
\begin{tabular}{cc|c|c|}
 &  & \multicolumn{2}{c}{P2} \\
cline{3-4}
 &  & L & R \\
cline{2-4}
\multirow{2}{*}{P1} & U & 4,18 & 6,7 \\
cline{2-4}
 & D & 8,0 & 8,11 \\
cline{2-4}
\end{tabular}
a) Construct the Bayesian normal-form representation of the game.
b) Find all Bayesian Nash equilibria of this game.

In the following incomplete information game, player 1 (P1) selects between U and D, and player 2 (P2) selects between L and R. Player 1 knows which game is being played, player 2 doesn't. The probability that they are playing the game on the left bimatrix is p = (1)/(2), and this is common knowledge.

2cP2

cline3-4
L R

cline2-4
2*P1 U 15,18 6,7

cline2-4
D 8,0 8,11

cline2-4

2cP2

cline3-4
L R

cline2-4
2*P1 U 4,18 6,7

cline2-4
D 8,0 8,11

cline2-4

a) Construct the Bayesian normal-form representation of the game.
b) Find all Bayesian Nash equilibria of this game.

Added by Monique A.

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