Normal form games

An $n$-person, finite, normal form game is a tuple $(N,A,u)$ where:

• $N$ is a finite set of players
• $A=A_1\times \dots \times A_n$ where $A_i$ is a finite set of actions available to $i$ Each $a=(a_1,\dots ,a_n)\in A$ is an action profile.
• $u=(u_1,\dots ,u_n)$ where $u_i:A\mapsto \mathcal{R}$ is a real-valued utility function for $i$.

Represented by $n$-dimensional matrix.

We analyse games in terms of strategies, that is what agents decide to do. An agent’s strategy set is its set of available choices.