Multiagent Systems

Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 225/731
3. Decision Making (1) 3. (Im-) Perfect Information
The following definition covers a game as a tree:
Definition 3.26 (Extensive form Games, Perfect Inf.)
A finite perfect information game in extensive form is a
tuple G = 〈A, A, H, Z, α, ρ, σ, µ 1 , . . . , µ n 〉 where
A is a set of n players, A is a set of actions
H is a set of non-terminal nodes, Z a set of terminal
nodes, H ∩ Z = ∅,
α : H → A assigns to each node a set of actions,
ρ : H → N assigns to each non-terminal node a player
who chooses an action at that node,
σ : H × A → H ∪ Z assigns to each (node,action) a
successor node (h 1 ≠ h 2 implies σ(h 1 , a 1 ) ≠ σ(h 2 , a 2 )),
µ i : Z → R are the utility functions.