1 Deterministic Game Trees with Complete Information
From Graph Theory we begin with some directed tree \(T\) where each non-terminal vertex of \(T\) is controlled by a player who will make a moveat the vertices she owns. If \(v\) is a vertext controlled by player \(P\), then out-edges from \(v\) will correspond to the possible moves player \(P\) can take. The terminal vertices will represent end-game conditions and each will be assigned a payoff amount for each player of the game. In this case we further assume there will be no chance moves and all playerse will know precisely who is moving and what their move is.
Definition (Player Vertex Assignment)