Since I have it, here's what de Forest Research had to say about the issue in an October 14, 1966 memo:
“Arena”, story outline by Gene Coon, and “Arena” a short story by Frederic Brown contain the following substantive similarities:
1. Aliens attacking earth colonies.
2. Imminent battle between earth and aliens.
3. Intervention of third, highly advanced intellect.
4. Instant transportation of Earthman and Alien, unarmed, to “arena” on an asteroid.
5. Single combat to determine which race survives.
6. The quality of mercy being the decisive factor in the outcome.
There are the following differences:
1. In the details of the story-telling, Act I and Act II of the Coon “Arena” recounting the first Earth-Alien encounters and the intervention of the third party is told in flashback in the Brown “Arena.”
2. The details of the “single combat.” In Coon “Area” the intervening intellect provides weapons which test only Kirk’s ingenuity. In Brown “Arena” the intervening intellect provides no weapons, but supplies a force field and raw materials to test the ingenuity.
3. In Coon “Arena” Kirk is merciful to the Alien which saves him. In Brown “Arena” Carson is merciful to the intelligent lizard which reveals to him the way through the barrier.
It is our opinion that Coon’s “Arena” is substantially similar to the copyrighted story “Arena” by Frederic Brown, and the airing of a screenplay from this outline without purchase of the Brown story would be actionable.
(The memo goes on with a two-page synopsis of the original Brown story, but since the original is available, I have omitted it).