Today I’m going to go over the terminology for different strategies of normal games. You can find the information I’m about to write in Essentials of Game Theory, but I will be elaborating on some important concepts and hopefully making these concepts easier to understand. I will be using some symbols from my previous post. See here if you want a refresher.

**Pure strategy**: A strategy that is a single action chosen by a player to use throughout the entire course of the game.**Mixed strategy**: A strategy that is a combination of different pure strategies where each pure strategy is played with a fixed probability (or a random probability) throughout the game. Defining to be the probability distribution over any set , the set of all mixed strategies, available to player in a normal game is . The set of the mixed strategies for all players in a game is the set of combinations of possible mixed strategies for each player (assuming we have players in a game): .**Expected utility**: The expected utility for player of a mixed strategy game is the sum of the expected utilities of each strategy multiplied by the probability of using that strategy. Given a mixed strategy , let be the probability action will be played. Let be the utility obtained by taking an action . Therefore, the expected utility, of a player with a mixed strategy profile composed of all the strategies for every player in the game can be defined as:

I will be talking about optimal utility functions and equilibrium in my next post.

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