In this LP, the second of our series on Game theory, we’ll learn everything there is about simultaneous games. These games, used when considering a game where players move or play their strategies simultaneously, are commonly used in many fields. From military strategies to collusion agreements, the analysis of these situations as simultaneous games can help us discover the best way to act. Finding Nash equilibria or knowing how to proceed to eliminate dominated strategies will get us the best outcome (and therefore help us win the game!).

We’ll consider that the rules of the game and each player’s payoffs are common knowledge, and that information is complete. Since moves are simultaneous, information will be imperfect. We’ll see the following definitions:

*Simultaneous games*, where we’ll learn the basics about these games.

**Nash equilibria and dominant strategies:**

*Prisoner’s dilemma*, the well-known game;

*Nash equilibria*, which are the best possible strategies given the other player’s;

*Dominant strategies* and elimination of dominated strategies, another way to proceed.

**Mixed strategies:**

*The Battle of the Sexes*, where a couple has to decide what to do over the weekend;

*Mixed strategies*, and how to analyse them where no clear equilibrium can be reached.

**Continuous strategies:**

*Cournot duopolies*, the best example of a simultaneous game where continuous strategies are used.