Conclusion
With the applet that we have built we show that it is possible to model agents playing a card game for which higher order reasoning is needed. This higher order reasoning is based on the knowledge of the agents. The knowledge of one agent can be viewed as a Kripke model, in which every possible combination of cards that the other players can have form an accessible Kripke world. For both choosing which cards to swap as for the signalling and calling kemps/anti-kemps part, this knowledge is used. However, the higher order reasoning is only needed for the latter in which agents need to decide whether a signal is real or fake.
Although our implementation of the game is very simplified, the complexity of the knowledge of the agents is already relatively complex. At the very start of a game, when an agent only knows its own cards and the cards on the table, there are 45 accessible Kripke worlds for an agent (6 unknown cards divided in 3 pairs of 2). This complexity shows that reasoning and in particular higher-order reasoning is not trival for agents, even in a (simplified) game like this.
Discussion
At the start of our project we did not expect that a very simplified card game would get as complex as our implementation eventually turned out to be. Especially updating the knowledge of the agents correctly, has given us problems because of this complexity. It is even possible that a few bugs still exist in this update process, however the agents show to be capable of playing the game successfully even with this sometimes maybe slightly imperfect knowledge.