Question 1 (1 point)
Eve is having dinner at a restaurant and she sees Adam enter the restaurant to order take out. Adam also sees Eve. They both choose between talking or not talking. If both choose to talk, then they eat together in the restaurant and both get a payoff of 0 . If Adam chooses to talk and Eve chooses to not talk, Adam gets a payoff of -2 and Eve gets a payoff of 1 . If Eve chooses to talk and Adam chooses to not talk, Eve gets a payoff of -3 and Adam gets a payoff of 1 . If both choose to not talk, they both get a payoff of 4 . The payc ff matrix for this game is shown below.
Find the dominant strategy for each agent (if one exists).
\begin{tabular}{|l|l|l|ll}
\hline \multirow{4}{*}{ Adam } & \multicolumn{4}{|c}{ Eve } \\
\cline { 2 - 5 } & & Talk & Don't Talk \\
& & & \\
\cline { 2 - 5 } & Talk & & 3,3 & \\
\hline
\end{tabular}

Step 1 ：The dominant strategy in a game theory context is the course of action that results in the highest payoff for a player, no matter what the other player does. In this scenario, we need to determine the dominant strategy for both Eve and Adam. First, let's correct the payoff matrix based on the information given: \begin{tabular}{|c|c|c|} \hline & Eve Talks & Eve Doesn't Talk \\ \hline Adam Talks & 0,0 & -2,1 \\ \hline Adam Doesn't Talk & 1,-3 & 4,4 \\ \hline \end{tabular} Now, let's analyze the dominant strategy for each player: For Adam: - If Eve talks, Adam's best response is to not talk (payoff of 1 is greater than 0). - If Eve doesn't talk, Adam's best response is also to not talk (payoff of 4 is greater than -2). So, Adam's dominant strategy is to not talk. For Eve: - If Adam talks, Eve's best response is to not talk (payoff of 1 is greater than 0). - If Adam doesn't talk, Eve's best response is to not talk (payoff of 4 is greater than -3). So, Eve's dominant strategy is also to not talk. Therefore, the dominant strategy for both Adam and Eve is to not talk.