# Simultaneous game

Rock–paper–scissors is an example of a simultaneous game.

In game theory, a simultaneous game or static game[1] is a game where each player chooses their action without knowledge of the actions chosen by other players.[2] Simultaneous games contrast with sequential games, which are played by the players taking turns (moves alternate between players). In other words, both players normally act at the same time in a simultaneous game. Even if the players do not act at the same time, both players are uninformed of each other's move while making their decisions.[citation needed][3] Normal form representations are usually used for simultaneous games.[citation needed] Given a continuous game, players will have different information sets if the game is simultaneous than if it is sequential because they have less information to act on at each step in the game. For example, in a two player continuous game that is sequential, the second player can act in response to the action taken by the first player. However, this is not possible in a simultaneous game where both players act at the same time.

Rock-paper-scissors, a widely played hand game, is an example of a simultaneous game. Both players make a decision without knowledge of the opponent's decision, and reveal their hands at the same time. There are two players in this game and each of them has three different strategies to make their decision; the combination of strategy profiles forms a 3×3 table. We will display Player 1's strategies as rows and Player 2's strategies as columns. In the table, the numbers in red represent the payoff to Player 1, the numbers in blue represent the payoff to Player 2. Hence, the pay off for a 2 player game in rock-paper-scissors will look like this:

Player 2

Player 1
Rock Paper Scissors
Rock
0
0
1
-1
-1
1
Paper
-1
1
0
0
1
-1
Scissors
1
-1
-1
1
0
0

Even though simultaneous games are normally represented in normal form, it can be represented using extensive form too. However, in an extensive form, we must draw one player’s decision before that of the other, but such representation does not correspond to the actual timing of the players’ decisions. It is important to note that the key to modeling simultaneous game in the extensive form is to get the information sets right. A dashed line between nodes in the extensive form representation of a game represent information asymmetry and specify that, during the game, a party cannot distinguish between the nodes. [4]

Examples of Simultaneous Games [4]

The prisoner's dilemma is also an example of a simultaneous game. Some variants of chess that belong to this class of games include synchronous chess and parity chess.[5]