You can always assume all participants lied about how the game went. Just add an implicit "assuming they didn't, ..." and the discussion is still valid.
At that point any discussion is moot though, since the only point of discussion is "what exact argument as used to convince", yet if both parties lied, then there is no such argument in the first place.
Since neither party is going to disclose the exact arguments, this discussion is still equivalent to "what arguments could be used to convince..." and you can have it regardless of whether or not the parties lied about the experiment's result.