Consider two restaurants, R1 and R2, simultaneously decide what sort of cuisine they will focus on, Thai (T) or Vietnamese (V). If both opt for T, the payoffs are 10 each. If both opt for V, the payoffs are 20 each. If R1 plays T and R2 V the payoffs are (30, 40). If R1 plays V and R2 T, the payoffs are (50, 60) for R1 and R2, respectively. What are the Nash equilibria?Group of answer choices(V, V)(T, T)(T, T) and (V, V); this is a coordination game(T, V) and (V, T); this is a coordination game.None of the above.
Question
Consider two restaurants, R1 and R2, simultaneously decide what sort of cuisine they will focus on, Thai (T) or Vietnamese (V). If both opt for T, the payoffs are 10 each. If both opt for V, the payoffs are 20 each. If R1 plays T and R2 V the payoffs are (30, 40). If R1 plays V and R2 T, the payoffs are (50, 60) for R1 and R2, respectively. What are the Nash equilibria?Group of answer choices(V, V)(T, T)(T, T) and (V, V); this is a coordination game(T, V) and (V, T); this is a coordination game.None of the above.
Solution
To find the Nash equilibria, we need to identify the situations where neither restaurant has an incentive to unilaterally change their strategy given the other restaurant's strategy.
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(V, V): If both restaurants choose V, the payoffs are 20 each. Neither restaurant can improve their payoff by unilaterally changing their strategy to T (as the payoff would decrease to 30 for R1 and 40 for R2), so (V, V) is a Nash equilibrium.
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(T, T): If both restaurants choose T, the payoffs are 10 each. Neither restaurant can improve their payoff by unilaterally changing their strategy to V (as the payoff would increase to 50 for R1 and 60 for R2), so (T, T) is not a Nash equilibrium.
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(T, V): If R1 chooses T and R2 chooses V, the payoffs are (30, 40). R1 could improve their payoff by unilaterally changing their strategy to V (as the payoff would increase to 50), so (T, V) is not a Nash equilibrium.
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(V, T): If R1 chooses V and R2 chooses T, the payoffs are (50, 60). R2 could improve their payoff by unilaterally changing their strategy to V (as the payoff would increase to 20), so (V, T) is not a Nash equilibrium.
So, the only Nash equilibrium in this game is (V, V). Therefore, the correct answer is "(V, V)".
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