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Question
Microeconomics
Posted 9 months ago

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.
Mountain View
advertise don't advertise

Prarie
price high
\begin{tabular}{|l|l|}
\hline$1000,$1000\$ 1000, \$ 1000 & $2500,$500\$ 2500, \$ 500 \\
\hline$500,$2500\$ 500, \$ 2500 & $2000,$2000\$ 2000, \$ 2000 \\
\hline
\end{tabular}

A Nash equilibrium exists when

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

Related content
Game theory worked example from AP Microeconomics
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Answer from Sia
Posted 9 months ago
Solution
a
Definition of Nash Equilibrium: A Nash equilibrium occurs when each player in a game chooses the best strategy given the strategies chosen by the other players, and no player can benefit by changing their strategy unilaterally
b
Identifying Nash Equilibrium: To find the Nash equilibrium, we need to check each combination of strategies to see if any player can improve their payoff by changing their strategy while the other player's strategy remains unchanged
c
Analysis of Payoff Matrix: - If Prairie Glen prices high and Mountain View advertises, the payoffs are 1000,1000, 1000. If Prairie Glen changes to pricing low, its payoff becomes 500,whichisworse.IfMountainViewchangestonotadvertising,itspayoffbecomes500, which is worse. If Mountain View changes to not advertising, its payoff becomes 500, which is also worse. - If Prairie Glen prices high and Mountain View doesn't advertise, the payoffs are 2500,2500, 500. If Prairie Glen changes to pricing low, its payoff becomes 2000,whichisworse.IfMountainViewchangestoadvertising,itspayoffbecomes2000, which is worse. If Mountain View changes to advertising, its payoff becomes 1000, which is better. - If Prairie Glen prices low and Mountain View advertises, the payoffs are 500,500, 2500. If Prairie Glen changes to pricing high, its payoff becomes 1000,whichisbetter.IfMountainViewchangestonotadvertising,itspayoffbecomes1000, which is better. If Mountain View changes to not advertising, its payoff becomes 2000, which is worse. - If Prairie Glen prices low and Mountain View doesn't advertise, the payoffs are 2000,2000, 2000. If Prairie Glen changes to pricing high, its payoff becomes 2500,whichisbetter.IfMountainViewchangestoadvertising,itspayoffbecomes2500, which is better. If Mountain View changes to advertising, its payoff becomes 500, which is worse
d
Conclusion: The combination where Prairie Glen prices low and Mountain View doesn't advertise (2000,2000, 2000) is the Nash equilibrium because neither player can improve their payoff by unilaterally changing their strategy
Answer
Prairie Glen prices low and Mountain View doesn't advertise
Key Concept
Nash Equilibrium
Explanation
A Nash equilibrium is a situation where no player can benefit by changing their strategy while the other player's strategy remains unchanged. In this game, the combination where Prairie Glen prices low and Mountain View doesn't advertise is the Nash equilibrium because neither firm can improve their payoff by changing their strategy unilaterally.

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