Positional and Detection Games
When it comes to the interaction of two ore more parties with individual aims, it’s all about ﬁnding an appropriate strategy. In most cases, the individual aim boils down to detection of information about the general situation or about your opponents and improvement of your own position. This goal becomes most clear and speciﬁc in the ﬁeld of recreational games. In games like chess or tic-tac-toe, every player has complete information and the player’s position decides over win and loss. On the contrary, in games like poker every player tries to ﬁnd out the value of the other players’ hands to play accordingly. This uncertainty of the opponent’s hand is the factor that makes the game interesting. Since all results of this thesis are connected to the ﬁeld of game theory, it seems important to mention that this research ﬁeld is not about having fun with diﬀerent kinds of games, but, in the contrary, it’s about analysis of these games. The crucial diﬀerence between casual games and formal combinatorial games is that a combinatorial game is always assumed to be played by two players of inﬁnite computational power. If the considered game is of complete information, the outcome of the game is already determined before it even started. The variety of games that are analyzed in this work ranges from popular recreational games as Mastermind over network-formation games to purely abstract games on graphs or hypergraphs
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