Sia
Question
Microeconomics
Posted 8 months ago
Saoirse and Shae are playing a game and their two strategies are stand up and sit down. The payoffs they get from their strategies (measured in points) are given in the payoff matrix shown here. The first entry represents Saoirse's payoff and the second entry represents Shae's payoff.
\begin{tabular}{|c|c|c|c|}
\hline & \multicolumn{2}{|c|}{ Shae } \\
\hline & & stand & sit \\
\hline \multirow{2}{*}{ Saoirse } & stand & 7,20 & 40,10 \\
\hline & sit & 10,3 & 20,20 \\
\hline
\end{tabular}
What is the Nash equilibrium for this game?
Choose 1 answer:
(A) Saoirse sits, Shae stands
(B) Saoirse stands, Shae sits
(c) Saoirse stands, Shae stands
(D) Saoirse sits, Shae sits
(E) There is no Nash equilibrium in this game
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Answer from Sia
Posted 8 months ago
Solution
a
Identify Dominant Strategies: A dominant strategy is one that results in the highest payoff for a player, regardless of the opponent's action. For Saoirse, if Shae stands, Saoirse gets 7 points by standing and 10 points by sitting. If Shae sits, Saoirse gets 40 points by standing and 20 points by sitting. Therefore, Saoirse's dominant strategy is to stand. For Shae, if Saoirse stands, Shae gets 20 points by standing and 10 points by sitting. If Saoirse sits, Shae gets 3 points by standing and 20 points by sitting. Therefore, Shae's dominant strategy is to sit
b
Check for Nash Equilibrium: A Nash equilibrium occurs when each player's strategy is optimal given the other player's strategy. From the dominant strategies identified, Saoirse stands and Shae sits. The payoff for this combination is (40, 10)
Answer
(B) Saoirse stands, Shae sits
Key Concept
Nash Equilibrium
Explanation
The Nash equilibrium is the strategy combination where each player's strategy is optimal given the other player's strategy. In this game, Saoirse's dominant strategy is to stand, and Shae's dominant strategy is to sit, resulting in the Nash equilibrium (40, 10).
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