If a player announced his retirement from international sports, Can he get back his retirement and play?
Who will decide on that(either the player or the country's sports authorities)?
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In short Yes.
There are many examples of retired players who made a "comeback".
When a player decides to retire it is his or her personal decision, they can do whatever they decide to do.
I don't know anything about Cricket so I will refer to your question in general:
In case the player decides to do a "comeback" we can divide the "comeback" to 2 categories:
Personal sports (Like Tennis) - The player can register to play in the tournament like any other "unretired" player, e.g. Kim Clijsters who announced her retirement from professional tennis on 2007 and made a comeback on 2009 and even returned to 1st place in the WTA rankings.
Team sports (Like Basketball) - The player can announce a "comeback" and will need to find a team that will want him, or that his international team will called him up to play like every other Free Player. The best example is Michael Jordan who retired 3 times! 2 from Basketball and 1 from Baseball.
You can read about other athletes who made a comeback at the following discussion.
Referring to your focusing on Cricket and international performance I found this player: Brad Hogg as an example to a player who retire from international cricket on 27 February 2008 and made his comeback 2 years later On 1 February 2012 representing Australia at the Sydney Olympic Stadium in a Twenty20 international against India.