Nobel prize in literature for the year 2013 was awarded to:

The correct option is Alice munro.

Explanation:
The Nobel Prize in Literature for the year 2013 was awarded to the Canadian author Alice Munro, who was described by the Swedish Academy as the "master of the contemporary short story." She is widely celebrated for her finely crafted short stories that explore human relationships and complex moral dilemmas set in rural and small-town Canadian settings.

Brief overview of other options:
• Mo Yan: Awarded the Nobel Prize in Literature in 2012.
• James E. Rothman: Awarded the Nobel Prize in Physiology or Medicine in 2013 (shared with Randy W. Schekman and Thomas C. Südhof).
• Lars Peter Hansen: Awarded the Nobel Memorial Prize in Economic Sciences in 2013 (shared with Eugene F. Fama and Robert J. Shiller).