These two works, A Room of One's Own by Virginia Woolf and The Hunger Games by Suzanne Collins, do not--at least on the surface--seem to have much of anything in common. A closer look does reveal several points of comparison as well as some significant points of contrast.
Obviously both works were written by females, and both works feature women protagonists. Games features Katniss, a young woman who sacrificially sets herself up as a potential savior of her sister as well as all the people of her district. Room features many women, most of whom succeed in some fashion despite significant oppression and even death, and depicts them as heroes, as well. Katniss is a skilled archer, hunter, and trapper; Woolf's heroines are skilled in significantly different ways. For example, Mary Beton leaves the narrator an inheritance so she is free to write, and Judith Shakespeare demonstrates an artistic genius equal to her "brother" William.
One theme that quickly becomes evident in Games is that a female is as capable as any male in terms of performance, intelligence, and skill; the same theme is evident in Room, though the range of skills in her essay is less physical and therefore less obvious. Both works make the case that when women are given the same opportunities as their male counterparts, they will demonstrate the same--or greater--level of achievement.
Another theme which can be found in both works is the contrast between the privileged class and the underprivileged class. In Games, that theme is demonstrated by money, as in the contrast between the Capitol and District 12. In Room, that theme is demonstrated by gender, as in the contrast between what men are given and what women must fight to get. (This is also a point of contrast, since one work deals with money and one with gender.) She compares the food men are served at male-only universities to the food women are served at female-only universities, and she says that men "feast" and women "sup." Her conclusion is that
[o]ne cannot think well, love well, sleep well, if one has not dined well.
Food is also a symbol in both works, a symbol of affluence in Games and a symbol of power in Room.
One other theme is survival. In Games it is overt; in Room it is implied, since women have overcome adversity to succeed--including Woolf herself.
In contrast, Games is a novel and Room is a collection of essays which can be read together but do not tell one cohesive story. Katniss's skills are appreciated and applauded by everyone who knows her or sees her in the Games; the skills Woolf's women have are not often appreciated by anyone other than Woolf and the readers to whom Woolf hopes to connect. Katniss wins her challenges and receives the accolades of her world for her victory; most of the women in Room die without ever having achieved the appropriate (or equivalent) recognition for their accomplishments.
Of course the obvious elements such as setting and style are completely different, as well. Games is a dystopian novel set in a futuristic world (presumably America); Room is a mix of fact and fiction which is clearly focused on British authors and circumstances. Games expresses its themes more subtly as they are woven into the story; Room's themes are more overt because the narrator's commentary is more pointed and obvious.
While they are distinctly different works written in distinctly different genres, The Hunger Games and A Room of One's Own do share some similar elements.