Two drivers are running late to work and approach a four-way stop at the same ti

Question

Two drivers are running late to work and approach a four-way stop at the same time. Both drivers consider running the stop sign so that he can make it to work on time. However, if both drivers run the stop sign, they crash into each other resulting in zero happiness for each of them. Happiness can be measured on a scale of 0 to 5. A payoff of 0 gives you the least amount of happiness and a payoff of 5 gives you the most happiness. Driver 1 and Driver 2 face the following payoff matrix as they decide whether to run the stop sign or to stop: Does Driver 1 have a dominant strategy? If yes, what is it? Does Driver 2 have a dominant strategy? If yes, what is it? Find the Nash equilibria.

Explanation / Answer

ans a)

driver 1 doesn't have dominant strategy. if driver 2 chooses to run, then driver 1 is better off when he stops whereas if driver 2 chooses to stop, then driver 1 is better off when he chooses to run.

ans b)

driver 2 doesn't have dominant strategy. if driver 1 chooses to run, then driver 2 is better off when he stops whereas if driver 1chooses to stop, then driver 2 is better off when he chooses to run.

c) no dominant startegy means no nash equilibrium

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