Definitions of give up:

• verb:   allow the other (baseball) team to score

  Example: "Give up a run"

• verb:   give up with the intent of never claiming again
• verb:   lose or lose the right to by some error, offense, or crime
• verb:   give up what is not strictly needed
• verb:   stop maintaining or insisting on; of ideas, claims, etc.

  Example: "Both sides have to give up some calims in these negociations"

• verb:   give up in the face of defeat of lacking hope; admit defeat
• verb:   give up or agree to forego to the power or possession of another
• verb:   refrain from consuming
• verb:   relinquish possession or control over
• verb:   leave (a job, post, post, or position) voluntarily
• verb:   put an end to a state or an activity
• verb:   part with a possession or right