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.

this seems to be in the wrong category. but i'll take some free points my dude

posting this in wrong category will result in people seeing it who won't know the answer.

a  social news website  is an  internet  website  that features  user-posted stories. such stories are ranked based on popularity, as voted on by other users of the site or by website administrators. users typically comment online on the news posts and these comments may also be ranked in popularity. since their emergence with the birth of  web 2.0, social news sites have been used to link many types of information, including news, humor, support, and discussion. all such websites allow the users to submit content and each site differs in how the content is moderated. on the  slashdot  and  fark  websites,  administrators  decide which articles are selected for the front page. on  reddit  and  digg, the articles that get the most votes from the community of users will make it to the front page. many social news websites also feature an online comment system, where users discuss the issues raised in an article. some of these sites have also applied their voting system to the comments, so that the most popular comments are displayed first. some social news websites also have a  social networking  function, in that users can set up a user profile and follow other users' online activity on the website.