Creating and updating Kripke models for multi-agent games with imperfect information against Nature

Sammanfattning: Higher-order knowledge can be crucial when playing a game. Information about the history of the game can also be important. Hintikka’s world is a tool that uses Kripke models to visualize higher-order knowledge for various games. The Kripke models represent possible states a game can be in, and which agents can separate what states. Hintikka’s world is, however, limited in what games it can display higher-order knowledge for, and it does not display the history of the games. One class of games it does not have the theoretical framework for visualizing higher-order knowledge for is multi-agent games with perfect information against Nature (MAGIIAN). This report, therefore, investigates how the framework behind Hintikka’s world can be adapted to histories of MAGIIAN games. In MAGIIAN games, a team of agents cooperates towards a common goal, which is common in many games. The result of the project is two definitions. The first defines how an initial Kripke model can be created from a MAGIIAN by using the MAGIIANs initial location as one possible world, together with the locations indistinguishable from the initial location for any agent. The relation consists of all worlds any agent cannot differentiate, and the labelling is the same as the world. The second definition defines how the Kripke models can be updated after a joint action of the agents. For the updated Kripke models, the possible worlds are the possible worlds from the previous model combined with the joint action taken and the locations that action leads to. The relation consists of all worlds any agent cannot differentiate, and the labelling is the last location in the history. These two definitions enable the implementation of histories of MAGIIAN games in Hintikka’s world in the future.