Hamlet asks Ros and Guil this question in the play. Companies of actors did not like to travel; their makeshift theatres in small country towns could not hold the audiences the city theatres could, and the towns did not have enough people to supply such audiences. Therefore revenues were down, and costs (which included the costs of transport for the actors, their costumes and props) were up. Many theatre companies went broke by doing it. Hamlet sums this up by saying "Their residence, both in
reputation and profit, was better both ways". Rosencrantz says that it is because of the new innovation which is stealing their city audiences. Which innovation? Companies of child actors, says Rosencrantz, "an eyrie of children, little eyases, that cry out on the top of question and are most tyrannically clapp'd for't. These are now the fashion." Shakespeare was alluding to the companies of child actors who were very popular around the turn of the century, especially the Children of the Chapel and the Children of St. Paul's
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Hamlet asks the players to perform a specific play containing the murder of Gonzago. He also requests that they insert specific lines that he created himself.
Hamlet asks the Players to perform a play called "The Murder of Gonzago." In it, a guy called Gonzago gets murdered. The players put on this play, with the first player playing the part of Gonzago, although he is not referred to by name.
All the world is a stage and men and women are merely the players (Hamlet)
Hamlet doesn't actually stage a play called The Mousetrap. He asks the travelling players (The Tragedians of the City) to put on The Murder of Gonzago, which is the real name of the play. Hamlet calls it the Mousetrap because his purpose in asking them to play it is to trap Claudius into a confession of guilt.
We don't know for sure, but it is likely that a group of travelling players visited Stratford when he was younger.