Coke and Pepsi each choose one of two prices: "Low" (P = $2) or "High" (P = $3). There are 50 buyers who will pick the lowest price option. However, if the prices are the same, 25 will buy from Coke and 25 from Pepsi. For simplicity, assume there are no costs, so profit is just price times quantity. a. Draw the 2x2 payoff matrix and find Nash equilibrium.
b. Now assume that each company has 20 loyal buyers who buy their brand regardless of price. This leaves 10 non-loyal buyers that pick the less expensive option. Again, non-loyal buyers split evenly if the prices are the same. Draw the new payoff matrix and find Nash equilibrium.

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.