Introducing Game Theory: A Graphic Guide (Introducing…)

Models are simple enough to analyze but still capture some important feature of the real-world problem. A cleverly chosen simple model can help us learn something useful about the complex real-world problem.

Game theorists solve the Guessing Game in a similar fashion using iterative elimination of dominated strategies.
Remember that you’re looking for 2/3 of the average number entered into the contest. If all contestants were to pick the highest permissible number, 100, the average would be 100. Hence, no matter what one expects the average to be, it makes no sense to ever guess a number greater than 2/3 of 100, which is 67.
In other words, any strategy with a guess greater than 67 is dominated by 67. A strategy is dominated if it (in this case, a guess higher than 67) is worse than another strategy (guessing 67) regardless of what other players do. Hence, even if no one else is rational, all strategies with a guess greater than 67 can be eliminated.

vidual benefits at the expense of others.

Success in financial markets depends on being one step ahead of the crowd. If you can predict the behaviour of the average investor, you can make a killing

There are well-defined rules in chess. There are a limited number of options in each move

these cases, people’s actions are influenced by their expectations of others’ actions.

In economics, the decisions of firms are affected by their expectations of a competitor’s choice of product, price and advertising.

While the Battle of Sexes Game does not give conditions under which societies evolve into patriarchy (a society structured around male advantage), it does give an insight into a potential benefit of gender-based dominance. This may be one of the reasons why it is so difficult to move society to a fairer system.

Game theory is the study of strategic interaction. Strategic interaction is also the key element of most board games, which is where it gets its name. Your decision affects the other player’s actions and vice versa. Much of the jargon of game theory is borrowed directly from games. The decision makers are called players. Players make a move when they make a decision.

Rationality refers to players understanding the setup of the game and exercising the ability to reason.
Common knowledge of rationality is a more subtle requirement. Not only do we both have to be rational, but I have to know that you are rational. I also need a second level of knowledge: I have to know that you know that I am rational. I need a third level of knowledge as well: I have to know that you know that I know that you know I am rational. And so on to deeper and deeper levels. Common knowledge of rationality requires that we are able to continue this chain of knowledge indefinitely.