Undersökning av stabilisering och icke-stabilisering av MKBSC i fleragentsspel

Sammanfattning: There are constructions called KBSC and MKBSC. KBSC is used to expand a player’s knowledge of the conditions in a game graph, while MKBSC works the same but for game graphs with at least two players working together towards a common goal. If you apply MKBSC several times to a game graph, the construction can potentially stabilize and there is no longer any point in running MKBSC. This report examines various multiplayer game graphs using a MKBSC tool written in Python. Possible explanations are then given as to why stabilization occurs or not intuitively based on the resulting iterated game graphs and with the help of mathematical notations that are usually being used in relation to MKBSC. The resulting findings show that the graphs generally tend to stabilize as long as there are not a number of conditions that are being fulfilled. These conditions include that there are at least three nodes where you can get from one node to another (though not necessarily with the use of a single action), there are partially overlapping observations for the players in the game and there is an uncertainty for the players about which upcoming state their individual choice of action leads to. In addition, the initial state of the game graph can affect whether or not MKBSC stabilizes.