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Betty and John are opening a restaurant together. To proceed with the project two choices must be made: the type of restaurant and the location. Since Betty and John don't agree on where/what store to open, they've divided the decision into two parts. Betty will choose the type of restaurant and John the location. The payoff matrix is presented below.

Strip Mall Arts District Business District
Steak house 1, 0 4, 4 7, 3
Italian 2, 1 5, 0 1, 0
Thai 0, 4 3, 5 6, 9

What is the Nash-Equilibrium?
a. (Italian, Strip Mall)
b. (Thai, Business District)
c. (Steak house, Business District)
d. (Tahi, Arts District)

User MattSlay
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1 Answer

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Final answer:

The Nash Equilibrium for Betty and John's restaurant type and location decision is (Thai, Business District), where both parties achieve their highest payoffs and have no incentive to change their strategies.

Step-by-step explanation:

The Nash Equilibrium in this scenario is option b, which is (Thai, Business District). In a Nash Equilibrium, no player can benefit by changing their strategy while the other players keep theirs unchanged. To identify the equilibrium, we look for the best response for each player given the other player's action.

By examining the payoff matrix, we can find the Nash Equilibrium by comparing the benefits for each type of restaurant against the possible locations. Focusing on the payoffs, for Betty, the Thai restaurant in the Business District offers the highest payoff (6). For John, locating in the Business District when Betty chooses a Thai restaurant gives him the highest payoff (9).

Both Betty and John have no incentive to change their decision once they choose Thai and Business District, respectively, hence it is the Nash Equilibrium. This means that if Betty is committed to a Thai restaurant, John's best response is to choose the Business District; and if John is committed to the Business District, Betty's best response is to opt for a Thai restaurant. No other combination offers a better payoff to both players simultaneously, as required by the Nash Equilibrium concept.

User Naser Mirzaei
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