This question is from " Networks, Crowds, and Markets: Reasoning about a Highly Connected World" textbook in chapter 6 Say whether the following claim is true or false, and provide a brief (1-3 sentence) explanation for your answer. Claim: If player A in a two-person game has a dominant strategy sA, then there is a pure strategy Nash equilibrium in which player A plays sA and player B plays a best response to sA.

If either player had a strictly dominant strategy, then she would have to play that strategy in both Nash equilibria in pure strategies; you can’t play a strictly dominated strategy in a Nash equilibrium. So if player i has a strictly dominant strategy, then she must play it in both Nash equilibria. But since the other player, j, isn’t indifferent between any two outcomes, j cannot be indifferent between the two Nash equilibria in pure strategies. Since j strictly prefers one Nash equilibrium to the other, and since i plays the same strategy in both NE, j would deviate from the NE that she likes less to the one she likes more. Thus the NE that j likes less cannot be a NE, and we’ve reached a contradiction. We conclude that neither player can have a strictly dominant strategy.

yes the ansewer is c bc you can look it up!

given the lack of choices, i'm gonna wing it and say that pushing your car off a cliff might not be the best idea. your car might sustain damage from the fall and will probably result in the car being too damaged to jump start.

if that's not good enough, avoid filling the car with bees. bees might get agitated when trapped or during the moving process, and might result in death or painful stings that will make jump starting your car very difficult. but in the event that you do choose to fill your car with bees, remember to wear protective gear!