So this little game actually amplifies the distinction between "game theory" and (let's call it) 'relationship theory'. In the former you rely on strategy. In the latter, you rely on established trust.

You run the game once and at the end you are given 'character' headsup on the participants. Next time around playing the same game, you know who is who.

p.s. In effect the distinction can be generalized as 'depth of priors' for the 'bayesian game'.