Sia
Question
Microeconomics
Posted 6 months ago
Theo and Addy are deciding what toys to pick out at the toy store. Depending on what toys they pick, they can play different games together, but they can't coordinate their choices.
The matrix below shows the payoff in units of utility from each possible outcome. Theo's utility is the first entry and Addy's utility is the second entry.
\begin{tabular}{|c|c|c|c|}
\hline & \multicolumn{2}{|c|}{ Addy } \\
\hline & & \begin{tabular}{c}
toy \\
gas pump
\end{tabular} & \begin{tabular}{l}
jump \\
rope
\end{tabular} \\
\hline \multirow{2}{*}{ Theo } & toy food & 10,20 & 3,10 \\
\hline & ball & 3,7 & 4,9 \\
\hline
\end{tabular}
How many Nash equilibria are there in this game?
Choose 1 answer:
(A) two
(B) one
(c) three
(D) zero
(E) four
Related content
Game theory worked example from AP Microeconomics
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Answer from Sia
Posted 6 months ago
Solution
a
Identifying Nash Equilibria: A Nash equilibrium occurs when each player's strategy is optimal given the other player's strategy. We need to check each cell in the payoff matrix to see if both players are making the best possible choice given the other player's choice
b
Analyzing Payoff Matrix:
- For Theo choosing "toy food" and Addy choosing "toy gas pump" (10, 20):
- Theo's best response to Addy's "toy gas pump" is "toy food" (10 > 3).
- Addy's best response to Theo's "toy food" is "toy gas pump" (20 > 10).
- This is a Nash equilibrium.
- For Theo choosing "toy food" and Addy choosing "jump rope" (3, 10):
- Theo's best response to Addy's "jump rope" is "ball" (7 > 3).
- This is not a Nash equilibrium.
- For Theo choosing "ball" and Addy choosing "toy gas pump" (3, 7):
- Theo's best response to Addy's "toy gas pump" is "toy food" (10 > 3).
- This is not a Nash equilibrium.
- For Theo choosing "ball" and Addy choosing "jump rope" (4, 9):
- Theo's best response to Addy's "jump rope" is "ball" (4 > 3).
- Addy's best response to Theo's "ball" is "jump rope" (9 > 7).
- This is a Nash equilibrium
Answer
Two
Key Concept
Nash Equilibrium
Explanation
A Nash equilibrium occurs when each player's strategy is optimal given the other player's strategy. In this game, there are two Nash equilibria: (toy food, toy gas pump) and (ball, jump rope).
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