It is refreshing to see a question that is about an author's life and influence instead of about a particular work of literature! Slawomir Mrozek, a Polish journalist and playwright, was definitely influenced by Shakespeare's Hamlet. Mrozek wrote his play Tango virtually as a parody of the events in Shakespeare's Hamlet.
The same elements and events are nearly mirrored in Tango, as Poland experienced a revolt in his parent's lifetime. Much of Mrozek's work was influenced by the Stalinist regime and the communist ideas of that era in Poland's history. His writings are known to be referenced in the Theater of the Absurd, or Absurdist Fiction. I would assume, then, he was also influenced by the other writers of that movement as well.
This stye of writing is highly political in nature, and utilizes unrealistic or absurd scenarios. However, after his controversial works in Poland, Mrozek moved to Italy and France. During that time he began to criticize the Stalinist regime and communist values.
His works influenced both writers from the East and West as he at times commended the actions of the Political powers and then criticized the very powers he had at first supported. Much of Mrozek's work was written and produced for its shock value.