# Definition:Strategic Game

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## Definition

A **strategic game** is a game in which:

- $(1): \quad$ Each player chooses a strategy once per play
- $(2): \quad$ The move(s) of each player operates simultaneously. That is, when choosing a move, each player has any information about the move that another player will make.

It consists of:

- A finite set $N$ of players
- For each player $i \in N$, a non-empty set $A_i$ of moves available to player $i$
- For each player $i \in N$, a preference relation $\succsim_i$ on $A = \displaystyle \prod_{j \mathop \in N} A_j$ of player $i$.

## Also known as

Some sources, for example 1944: John von Neumann and Oskar Morgenstern: *Theory of Games and Economic Behaviour*, refer to a **strategic game** as a **game in normal form**.

## Sources

- 1994: Martin J. Osborne and Ariel Rubinstein:
*A Course in Game Theory*... (previous) ... (next): $1.2$: Games and Solutions - 1994: Martin J. Osborne and Ariel Rubinstein:
*A Course in Game Theory*... (previous) ... (next): $2.1$: Strategic Games: Definition $11.1$