There are k players, with player i having value vi > 0, i = 1,...,k. In every period, two of the players play a game, while the other k 2 wait in an ordered line. The loser of a game joins the end of the line, and the winner then plays a new game against the player who is first in line. Whenever i and j play, i wins with probability vi/(vi+vj) (a) Define a Markov chain that is useful in analyzing this model. (b) How many states does the Markov chain have? (c) Give the transition probabilities of the chain.