Brief Summary
This lecture from YaleCourses focuses on game theory and its real-world applications. The lecture starts by recapping the Prisoners' Dilemma and its relevance to various scenarios like joint projects, price competition, and environmental issues. It then introduces the formal ingredients of a game: players, strategies, and payoffs. The lecture explores the concepts of strictly dominated strategies, weakly dominated strategies, and the importance of understanding the rationality of other players in a game. The lecture concludes with a discussion of common knowledge and how it differs from mutual knowledge.
- The Prisoners' Dilemma is a game where individuals have an incentive to act in their own self-interest, even if it leads to a worse outcome for everyone involved.
- The formal ingredients of a game include players, strategies, and payoffs.
- Understanding the rationality of other players is crucial for predicting their actions and making informed decisions in a game.
- Common knowledge is a concept where everyone knows something, everyone knows that everyone knows it, and so on, creating an infinite chain of knowledge.
Chapter 1. Recap of Previous Lecture: Prisoners' Dilemma and Payoffs
The lecture begins by reviewing the Prisoners' Dilemma, a game where two individuals are better off cooperating but have an incentive to defect. The professor provides real-world examples of the Prisoners' Dilemma, such as joint projects, price competition, and environmental issues like global warming. He emphasizes that communication alone is not enough to solve the dilemma and that changing the payoffs through contracts, treaties, or regulations is necessary.
Chapter 2. The Formal Ingredients of a Game
This chapter introduces the formal components of a game. The professor defines players, strategies, and payoffs, using notation to represent them. He explains that players are the individuals involved in the game, strategies are the actions they can take, and payoffs are the outcomes they receive based on their choices.
Chapter 3. Weakly Dominant Strategies
The lecture delves into the concept of weakly dominated strategies. A weakly dominated strategy is one where a player can always do at least as well, and sometimes better, by choosing another strategy. The professor illustrates this concept using the example of an invader choosing between an easy and a hard pass to attack a country. He explains that the easy pass weakly dominates the hard pass because the invader can always achieve the same or better outcome by choosing the easy pass.
Chapter 4. Rationality and Common Knowledge
This chapter explores the role of rationality and common knowledge in game theory. The professor argues that rational players, who aim to maximize their payoffs, will avoid playing dominated strategies. He then introduces the concept of common knowledge, which is the idea that everyone knows something, everyone knows that everyone knows it, and so on. The professor demonstrates how common knowledge of rationality can influence the outcome of a game, using the example of the numbers game played in the previous lecture.
Chapter 5. Common Knowledge vs. Mutual Knowledge
The lecture concludes by distinguishing between common knowledge and mutual knowledge. The professor explains that mutual knowledge simply means that everyone knows something, while common knowledge requires an infinite chain of knowledge where everyone knows that everyone knows it, and so on. He uses a hat experiment with two TAs to illustrate that mutual knowledge does not necessarily imply common knowledge. The professor emphasizes the importance of understanding the different levels of knowledge in game theory and how they can affect the outcome of real-world interactions.
