Prairie Glen and Mountain View sell flavored fizzy water in a market where they are the only two sellers. Each is considering what actions to undertake in the following week. The payoff matrix shown here shows each firm's daily profits for each combination of actions. The first entry represents Prarie Glen's payoff and the second entry represents Mountain View's payoff.
\begin{tabular}{|c|c|c|c|}
\hline & \multicolumn{2}{|c|}{\begin{tabular}{l}
Mountain \
View
\end{tabular}} \
\hline & & advertise & don't advertise \
\hline \multirow{2}{*}{\begin{tabular}{l}
Prarie \
Glen
\end{tabular}} & price high & $\$ 1000, \$ 1000$ & $\$ 2500, \$ 500$ \
\hline & price low & $\$ 500, \$ 2500$ & $\$ 2000, \$ 2000$ \
\hline
\end{tabular}

A Nash equilibrium exists when

Choose 1 answer:
(A) Prairie Glen prices high and Mountain View doesn't advertise
(B) there's no Nash equilibrium in this game
(c) Prairie Glen prices high and Mountain View advertises
(D) Prairie Glen prices low and Mountain View advertises
(E) Prairie Glen prices low and Mountain View doesn't advertise

Question

Prairie Glen and Mountain View sell flavored fizzy water in a market where they are the only two sellers. Each is considering what actions to undertake in the following week. The payoff matrix shown here shows each firm's daily profits for each combination of actions. The first entry represents Prarie Glen's payoff and the second entry represents Mountain View's payoff.
\begin{tabular}{|c|c|c|c|}
\hline & \multicolumn{2}{|c|}{\begin{tabular}{l} 
Mountain \
View
\end{tabular}} \
\hline & & advertise & don't advertise \
\hline \multirow{2}{*}{\begin{tabular}{l} 
Prarie \
Glen
\end{tabular}} & price high & $\$ 1000, \$ 1000$ & $\$ 2500, \$ 500$ \
\hline & price low & $\$ 500, \$ 2500$ & $\$ 2000, \$ 2000$ \
\hline
\end{tabular}

A Nash equilibrium exists when

Choose 1 answer:
(A) Prairie Glen prices high and Mountain View doesn't advertise
(B) there's no Nash equilibrium in this game
(c) Prairie Glen prices high and Mountain View advertises
(D) Prairie Glen prices low and Mountain View advertises
(E) Prairie Glen prices low and Mountain View doesn't advertise

Accepted Answer

∻Solution∻ ‖ a ⋮ Identifying Nash Equilibrium: 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 unilaterally from their strategy. ‖ ‖ b ⋮ Analyzing Prairie Glen's Strategies: If Mountain View advertises, Prairie Glen's best response is to price high ($1000 vs $500). If Mountain View doesn't advertise, Prairie Glen's best response is to price high ($2500 vs $2000). ‖ ‖ c ⋮ Analyzing Mountain View's Strategies: If Prairie Glen prices high, Mountain View's best response is to not advertise ($500 vs $1000). If Prairie Glen prices low, Mountain View's best response is to advertise ($2500 vs $2000). ‖ ‖ d ⋮ Determining Nash Equilibrium: Combining the best responses from both firms, the Nash equilibrium is where Prairie Glen prices high and Mountain View doesn't advertise, as neither firm would benefit from changing their strategy unilaterally. ‖ ∻Answer∻ ⚹ (A) Prairie Glen prices high and Mountain View doesn't advertise ⚹ ∻Key Concept∻ ⚹ Nash Equilibrium in Game Theory ⚹ ∻Explanation∻ ⚹ A Nash equilibrium is reached when each firm's strategy is the best response to the other's strategy, and neither has an incentive to change their decision unilaterally. In this case, Prairie Glen will price high and Mountain View will not advertise, as changing these strategies would not increase either firm's profit given the other's strategy. ⚹◊What impact does advertising have on the pricing strategy of firms in the fizzy water market according to this payoff matrix?⍭ Generate me a similar question◊

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