0x142 Game-Theory

Classical Games

Definition (normal form game) A game in normal form consists of

• A (finite) number of players \(M = \{ a_1, ..., a_n \}\)
• A strategy set \(S_i\) assigned to each player \(i \in M\), the combination of all sets of strategies \(S=\prod_i S_i\) is called strategy space
• A utility/payoff function \(u_i: S \to R\) assigned to each player \(i \in M\) such that \(\forall s \in S: u_i(s) \in \mathbf{R}\)

Evolutionary Games

Evolutionary game theory encompasses Darwinian evolution, including competition (the game), natural selection (replicator dynamics), and heredity