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3. You and another driver reach a four-way stop intersection at the same time. The other driver is to your right and you are

Game Theory

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Answer #1

The payoff matrix can be shown as follows

Driver 2 Go Wait (-10,-10) (2,0) (0,2) (-2,-2) Driver 1 Go Wait

If driver 1 chooses to go, then driver 2 will wait since its payoff of 0 > -10. Then driver 1 will stick to its strategy and there will not be any deviation from any of the drivers. Hence, (Go, Wait) = (2,0) is a Nash equilibrium.

On the other hand, if driver 1 chooses to wait, then driver 2 will choose to go since its payoff of 2 > -2. Then driver 1 will stick to its strategy and there will not be any deviation from any of the drivers. Hence, (Wait, Go) = (0,1) is a Nash equilibrium.

As observed, there is no dominant strategy for any of the driver.

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