The most important part of the game is of course not only asking the right questions to the right person yourself but also looking at what the other players are saying to each other. Thus, is seems possible to describe the model of this game in terms of public announcement logic. For example all propositional atoms can be represented as p[i,j] = player[i] has diamond card[j] and each turn can be represented as public announcement.
In terms of Kripke models we have to model a couple of things. Firstly we need to model that if an agent responds, all the epistemic alternatives that become impossible are removed from the model. Let's say that agent 1 responds that he has two red cards. For the model this means that all the worlds where the agent does not have 2 cards are invalid and thus can be discarded. The model does not have to keep track if it knows which is the card that is hidden because at the end of the game only 1 world will remain possible and the hidden card in that world is the actual hidden card.