Multiagent Systems

of. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 191/731
3. Decision Making (1) 2. Non-coop Games
Definition 3.5 (n-Person Normal Form Game)
A finite n-person normal form game is a tuple
〈N, A, O, ϱ, µ〉, where
N = {1, . . . i, . . . , n} is a finite set of players.
A = 〈A 1 , . . . , A i , . . . A n 〉 where A i is the set of actions
available to player i. A vector a ∈ A is called action
profile. The elements of A i are also called pure
strategies.
O is the set of outcomes.
ϱ : A −→ O assigns each action profile an outcome.
µ = 〈µ 1 , . . . µ i , . . . µ n 〉 where µ i : O −→ R is a
real-valued utility (payoff) function for player i.