There are a couple of similarities between the stories that seem to be to be almost an homage to the earlier story "The Lottery." For one thing the names chosen by the authors are symbolic: in Jackson's short story there are characters whose last names are "Summers" and "Graves" and these names both speak to symbolism relevant to the story. "Summers" implies the repetition every season of the lottery, making it a yearly tradition akin to an agricultural festival. "Graves" is name that functions as a kind of foreshadowing because the lottery always results in one resident of the town being stoned to death by the others.
The symbolic nature of many of the names in The Hunger Games finds characters with names based upon the natural world, as well as names of Shakespeare characters and characters from mythology. The names tend to be suggestive rather than explicit in this way. Katniss's younger sister is named Primrose, which denotes her fragility and youth, emphasizing Katniss' desire to protect her. Their last name "Everdeen" suggests the concept of loyalty and steadfastness, "ever" meaning Katniss is constant and dependable. Some of the other Hunger Games participants have mythological names such as the twins Castor and Pollux, or from Shakespeare, such as President Coriolanus (from the play named after a Roman leader), or Cressida (from Troilus and Cressida). The use of names from these texts lends an air of myth and ancient history to the story, which has many disparate elements that give it a timeless quality that blends images reminiscent of the past and hinting at the future.
The other similarity between the two narratives lies in the central event referred to in the title of each; the lottery drawing and the Hunger Games are both spectacles and contests, designed to be games of chance. The element of fate figures strongly in the outcome, but both events are also designed and implemented by their respective governments, and the residents are forced to participate.