No, they do not. According to Dallas Latos, wife of Cincinnati Reds pitcher Mat Latos. Players are allowed 4 family tickets and 2 friends tickets to purchase at around 40% of their face value, which varies from ballpark to ballpark.
http://www.usatoday.com/story/gameon/2013/04/02/Baseball-players-buy-baseball-tickets/2047445/
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