Okay. First off, we want to avoid making any decision ourselves about what “would have” happened. We shouldn't try to assume who should have won. We have a scenario where no player has conceded (alternatively, you could say that there's an implied double concession, but the result is the same). That said, let's look at the options we have here, assuming that their stories check out. (When I say their stories check out, we often call this “investigation.” Simply put, it's making sure that what they've told you is what actually happened. Humans have a tendency to remember what is convenient for us).
First, try to see if you can get the players to agree on a concession. Often times, by having the players talk it out, they can come to an agreement on what should have happened. While this may not work in tournament with higher prize payouts or other rewards, I find that this option is usually the best in a scenario like this.
However, if that fails, then our other solution is to call the game a draw and have them play another game (assuming time hasn't been called for the round). Since the game had ended with no declared winner, this is the next best option. The players may not appreciate this option, since they both believed they had won, so take this time to educate them about being clearer in their communication.
Edited Peter Richmond (May 19, 2014 09:28:36 AM)