A fight to the death. Yeah, that's what he was told before they tossed him into this little circus. Frankly, Joel doesn't give a shit what this is, as long as he can find Ellie. He always assumes most everyone is trying to kill him, anyway. It's a fact of life, back home.

So this guy mostly doesn't have anything to say that Joel hasn't already figured out for himself, except - I believe she is alive. On one hand, he could be saying that just to appease him, just to save his own skin. On the other, well -

"What makes you think she's alive?" he asks, voice still low and gruff. He probably won't kill this guy, either way - he's not enough of a threat, it would be pointless - but he keeps the threat in his tone, anyway. Names are less important to him than information.