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) one
(B) three
(C) two
(D) zero
(E) four

Question

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) one
(B) three
(C) two
(D) zero
(E) four

Accepted Answer

∻Solution∻ ‖ a ⋮ Identifying Nash Equilibria: A Nash equilibrium occurs when each player's strategy is optimal given the other player's strategy, and no player has an incentive to deviate from their chosen strategy. ‖ ‖ b ⋮ Analyzing Theo's Best Responses: For each of Addy's choices, determine Theo's best response. If Addy chooses the toy gas pump, Theo's best response is toy food (10 > 3). If Addy chooses the jump rope, Theo's best response is the ball (4 > 3). ‖ ‖ c ⋮ Analyzing Addy's Best Responses: For each of Theo's choices, determine Addy's best response. If Theo chooses toy food, Addy's best response is the toy gas pump (20 > 10). If Theo chooses the ball, Addy's best response is the jump rope (9 > 7). ‖ ‖ d ⋮ Determining Nash Equilibria: A Nash equilibrium is present where both players are making their best responses simultaneously. From the previous steps, we see that the combination (toy food, toy gas pump) and (ball, jump rope) are Nash equilibria. ‖ ∻Answer∻ ⚹ (C) two ⚹ ∻Key Concept∻ ⚹ Nash Equilibrium ⚹ ∻Explanation∻ ⚹ A Nash equilibrium is a situation where no player can benefit by changing their strategy while the other players keep theirs unchanged. In this game, there are two Nash equilibria. ⚹◊What is the definition of Nash equilibrium in game theory?⍭ Generate me a similar question◊

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