That's the Diploma Thesis I've submitted in 2011 for completion of the Computer Science studies in Germany. It all started as an affection to Poker and WSOP glamour - which soon enough led me to questions about the mathematical nature of the game. Enjoy.
Language: English
The Problem: You can describe a round of Poker as a beautiful tree using Extensive Form. Only the tree will be too huge. Imagine the standard procedure of solving it (= finding an optimal strategy). It goes like this: you compute a matrix from the tree (appr. the size n times n, where n is the number of nodes in the tree) and then run Simplex algorithm to solve this enormous linear maximization problem. It's a pain.
The Result: An extended form of Extensive Form is proposed, which allows to define certain patterns (very often seen in Poker, namely betting rounds) in a more adequate way. In that way, we make the tree much smaller. Then a simple definition of strategy and a Partial Sequential Equilibrium are proposed (in some ways, equivalent to Sequential Equilibrium in Extensive Form games). The solution is a bit constrained though and can only be used on simpler games, because certain imperfect information structures demand other definition of strategy/equilibrium.
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