Three boys A, B, and C are playing table tennis. In each game, two of the boys play against each other and the third boy does not play. The winner of any given game n plays again in game n + 1 against the boy who did not play in game n, and the loser of game n does not play in game n + 1. The probability that A will beat B in any game that they play against each other is 0.3, the probability that A will beat C is 0.6, and the probability that B will beat C is 0.8. Represent this process as a Markov chain with stationary transition probabilities by defining the possible states and constructing the transition matrix.