Game Theory

Game theory is a much younger tool than most of the others we have discussed so far and has become a large field of research. Here, we will just present two different games. These will get to represent the two different groups of games: normal form games and extensive form games.

The Basics of Game Theory

Game theory is used for analyzing how individual agents interact with each other. Depending on the structure, they may take into account how the other agents are choosing (or how they believe that they will choose), and then decide on their own strategy. This closely resembles the situation in many parlor games. Think, for instance, how the players act in chess: They only decide on their own moves, but they do so depending on how they believe that the opponent will respond. It is most often a bad strategy to hope that the opponent will not discover a trap. A better strategy is to assume that the opponent understandseverything that one understands oneself, and then base one’s strategy on that.

To turn this into a theory, we need to first define the basic building blocks. For a game to be a game in the relevant sense, we need players, rules, outcomes, and preferences over the outcomes. With chess, the players are “white” and “black,” the rules are the rules for chess, the usual outcomes are “white takes black’s king,” “black takes white’s king” or “draw.” The players’ preferences are usually that they prefer that they take the opponent’s king to a draw, and lastly that the opponent takes their king. In most games of game theory, we need to specify:

• The players. It could be individuals, firms, or countries. Often, there are only two or three players.
• Actions. All possible actions the different players can choose to do, for instance decide on quantity or price.
• Information. What each player knows at different stages of the game.
• Strategies. A strategy is a complete description of what a player will choose at each possible situation that could arise in a game. One can think of a strategy as a list. The list should be so exhaustive that player, and never actually have to decide anything by herself.
• Payoffs. The utility a player gets, given a certain outcome of the game.
  

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