73. There are k players, with player i having valueI mage,I mage. In every period, two of the players play a game. Whoever wins then plays the next game against a randomly chosen one of the other players (including the one who has just lost). Suppose that whenever i and j play, i wins with probability . Let denote the winner of game n.

(a) Give the transition probabilities of the Markov chain Image.

(b) Give the stationarity equations that are uniquely satisfied by the .

(c) Give the time reversibility equations.

(d) Find the proportion of all games that are won by j, Image.

(e) Find the proportion of games that involve player j as one of the contestants.