Summary 18. Imperfect information: information sets and sub-game perfection - YouTube (Youtube) www.youtube.com
11,330 words - YouTube video - View YouTube video
One Line
The text explains how imperfect information is incorporated into game theory through the use of information sets in a tree structure, highlighting its effects.
Slides
Slide Presentation (9 slides)
Key Points
- Imperfect information in game theory occurs when players cannot distinguish between certain nodes in a game tree.
- Information sets are used to represent lack of knowledge in game theory, and they are collections of nodes that a player cannot distinguish between.
- Perfect information games have information sets with only one node, while imperfect information games have information sets with more than one node.
- Subgame perfect equilibrium is a solution concept in game theory that combines the ideas of Nash equilibrium and backward induction.
- A subgame is a game within a game, and a subgame perfect equilibrium is an equilibrium that induces a Nash equilibrium in every subgame of the game.
Summaries
20 word summary
Imperfect information is introduced in game theory using information sets in a tree structure, demonstrating the impact of imperfect information.
69 word summary
This video introduces imperfect information in game theory, using information sets in a tree structure. Examples demonstrate backward induction and the impact of imperfect information. Information sets are defined as collections of nodes where players can't distinguish between them. The importance of determining what players know and when they know it is emphasized. Subgame perfect equilibrium combines Nash equilibrium and backward induction, ensuring consistency and believability in game analysis.
130 word summary
This video introduces the concept of imperfect information in game theory and how it can be represented using information sets in a tree structure. It presents examples of games to demonstrate the application of backward induction and the impact of imperfect information on outcomes. Information sets are defined as collections of nodes in the tree where players cannot distinguish between them. The video emphasizes the importance of determining what players know and when they know it. It also introduces the concept of subgame perfect equilibrium, which combines Nash equilibrium and backward induction. Subgame perfect equilibrium is defined as an equilibrium that induces a Nash equilibrium in every subgame of the game. The video concludes by highlighting the importance of subgame perfect equilibrium in ensuring consistency and believability in game analysis.
399 word summary
This video introduces the concept of imperfect information in game theory and how it can be represented using information sets in a tree structure. It explains that perfect information occurs when players can observe all previous moves, while imperfect information occurs when players cannot distinguish between certain nodes in the tree.
The video presents a simple game as an example, demonstrating how to solve it using backward induction. It then introduces a similar game with a change in information, where player 2 cannot distinguish between player 1 choosing up or middle. This leads to a different outcome, as player 1 now has an incentive to randomize between up and middle.
The concept of information sets is introduced as a way to represent this lack of knowledge. Information sets are defined as collections of nodes in the tree that a player cannot distinguish between. The video shows how to represent this in the tree by drawing a dotted line between the nodes.
The video defines perfect information as games where all information sets contain just one node, and imperfect information as games where information sets contain more than one node. It emphasizes the importance of determining what players know and when they know it.
In a more complex example, the video presents a game where player 1 has two choices, player 2 has three choices, and player 1 has a second chance to move under certain conditions. The video demonstrates how to determine strategies for each player and construct the matrix representation of the game.
The video provides an introduction to imperfect information and information sets in game theory, explaining how they can be used to represent strategic situations where players have limited knowledge. It demonstrates how to analyze and solve games with imperfect information using techniques such as backward induction and matrix representation.
The concept of subgame perfect equilibrium is introduced as a solution concept that combines the ideas of Nash equilibrium and backward induction. It is defined as an equilibrium that induces a Nash equilibrium in every subgame of the game.
The video provides examples to illustrate the application of subgame perfect equilibrium and concludes by emphasizing its importance as a solution concept that ensures consistency and believability in game analysis. It is presented as a tool to model games with both sequential and simultaneous moves and integrate ideas from the first and second halves of the course.
701 word summary
This video introduces the concept of imperfect information in game theory and how it can be represented using information sets in a tree structure. Perfect information occurs when players can observe all previous moves, while imperfect information occurs when players cannot distinguish between certain nodes in the tree.
The video presents a simple game as an example, where player 1 moves first and has three choices, and player 2 moves second and has two choices. The payoffs for the game are given. The video demonstrates how to solve this game using backward induction.
Next, the video introduces a similar game but with an important difference. In this new game, player 2 cannot distinguish between player 1 choosing up or middle. This change in information leads to a different outcome. Player 1 now has an incentive to randomize between up and middle. Player 2's choice is not as obvious in this game, as they cannot determine if they are in the upper or lower node.
The concept of information sets is then introduced as a way to represent this lack of knowledge. An information set is a collection of nodes in the tree that a player cannot distinguish between. The video shows how to represent this in the tree by drawing a dotted line between the nodes. Information sets must obey certain rules, such as not allowing a player to know which node they are in based on the number of choices available.
The video defines perfect information as games where all information sets contain just one node, and imperfect information as games where information sets contain more than one node. The key is to determine what players know and when they know it. The video provides examples of how to convert a tree into a matrix representation and vice versa.
In a more complex example, the video presents a game where player 1 has two choices, player 2 has three choices, and player 1 has a second chance to move if certain conditions are met. The video demonstrates how to determine the strategies for each player and constructs the matrix representation of the game.
The video provides an introduction to imperfect information and information sets in game theory, explaining how they can be used to represent strategic situations where players have limited knowledge. The video demonstrates how to analyze and solve games with imperfect information using techniques such as backward induction and matrix representation.
The video then introduces the concept of subgame perfect equilibrium as a solution concept that combines the ideas of Nash equilibrium and backward induction. It discusses a game with imperfect information and two players, where each player has two strategies. The video compares the payoffs for different strategy combinations and notes that some strategies lead to the same outcomes.
The focus shifts to finding the Nash equilibrium in the game. Best responses are determined for each player's strategy choices, and it is concluded that there are three Nash equilibria in the game. However, not all of these equilibria are plausible and consistent with backward induction.
The concept of subgame perfect equilibrium is introduced as a solution concept that addresses these issues. A subgame is defined as a game within a game, and it must satisfy three properties. The notion of subgame perfect equilibrium is defined as an equilibrium that induces a Nash equilibrium in every subgame of the game.
The video provides examples to illustrate the application of subgame perfect equilibrium. In one example, the entry game, it is shown that there are two subgames: the entire game itself and a smaller subgame within it. The equilibrium of the larger subgame is found by first determining the equilibrium of the smaller subgame and then considering the equilibrium of the whole game.
The video concludes by emphasizing the importance of subgame perfect equilibrium as a solution concept that combines the ideas of Nash equilibrium and backward induction. Subgame perfect equilibrium ensures that players will play a Nash equilibrium in every subgame, aligning with consistency and believability in game analysis. It is presented as a tool to model games with both sequential and simultaneous moves and to integrate the ideas from the first and second halves of the course.
966 word summary
In this video, the speaker introduces the concept of imperfect information in game theory and how it can be represented using information sets in a tree structure. The speaker explains that perfect information is when each player in the game can observe all previous moves, while imperfect information occurs when players cannot distinguish between certain nodes in the tree.
The speaker presents a simple game as an example, where player 1 moves first and has three choices (up, middle, down), and player 2 moves second and has two choices (left, right). The payoffs for the game are given. The speaker demonstrates how to solve this game using backward induction, where player 2's best response is to choose left if player 1 chooses down.
Next, the speaker introduces a similar game but with an important difference. In this new game, player 2 cannot distinguish between player 1 choosing up or middle. The speaker explains that this change in information leads to a different outcome. Player 1 now has an incentive to randomize between up and middle, as this gives them an expected payoff of 2, which is better than choosing down. The speaker points out that player 2's choice is not as obvious in this game, as they cannot determine if they are in the upper or lower node.
The concept of information sets is then introduced as a way to represent this lack of knowledge. An information set is a collection of nodes in the tree that a player cannot distinguish between. The speaker shows how to represent this in the tree by drawing a dotted line between the nodes. The speaker emphasizes that information sets must obey certain rules, such as not allowing a player to know which node they are in based on the number of choices available. The speaker also acknowledges that perfect recall is assumed in these games, although in reality, players may not have perfect memory.
The speaker then defines perfect information as games where all information sets contain just one node, and imperfect information as games where information sets contain more than one node. The speaker explains that what matters in these games is information, not time, and that the key is to determine what players know and when they know it. The speaker provides examples of how to convert a tree into a matrix representation and vice versa, highlighting that the same game can be represented differently depending on the order of moves.
In a more complex example, the speaker presents a game where player 1 has two choices (up, down), player 2 has three choices (left, middle, right), and player 1 has a second chance to move if certain conditions are met. The speaker demonstrates how to determine the strategies for each player and constructs the matrix representation of the game. The speaker concludes by noting that there are four strategies for player 1 and two strategies for player 2 in this game.
Overall, the video provides an introduction to imperfect information and information sets in game theory, explaining how they can be used to represent strategic situations where players have limited knowledge. The speaker demonstrates how to analyze and solve games with imperfect information using techniques such as backward induction and matrix representation.
In this video, the concept of subgame perfect equilibrium is introduced as a solution concept that combines the ideas of Nash equilibrium and backward induction. The video begins by discussing a game with imperfect information and two players, where each player has two strategies. The payoffs for different strategy combinations are compared, and it is noted that some strategies lead to the same outcomes. This redundancy is highlighted as an important aspect to consider in analyzing the game.
The focus then shifts to finding the Nash equilibrium in the game. Best responses are determined for each player's strategy choices, and it is concluded that there are three Nash equilibria in the game. However, it is pointed out that not all of these equilibria are plausible and consistent with backward induction. This leads to the recognition that a more refined notion of equilibrium is needed to deal with games that involve both sequential and simultaneous moves, as well as imperfect information.
The concept of subgame perfect equilibrium is introduced as a solution concept that addresses these issues. A subgame is defined as a game within a game, and it must satisfy three properties: it starts from a particular node, it comprises all successors of that node, and it does not break up any information sets. The notion of subgame perfect equilibrium is then defined as an equilibrium that induces a Nash equilibrium in every subgame of the game.
The video provides examples to illustrate the application of subgame perfect equilibrium. In one example, the entry game, it is shown that there are two subgames: the entire game itself and a smaller subgame within it. The equilibrium of the larger subgame is found by first determining the equilibrium of the smaller subgame and then considering the equilibrium of the whole game. In another example, a more complex tree is analyzed, and it is determined that the subgame perfect equilibrium is for player 1 to choose b, player 2 to choose down, and player 3 to choose right.
The video concludes by emphasizing the importance of subgame perfect equilibrium as a solution concept that combines the ideas of Nash equilibrium and backward induction. It is noted that subgame perfect equilibrium ensures that players will play a Nash equilibrium in every subgame, which aligns with the notion of consistency and believability in game analysis. The concept of subgame perfect equilibrium is presented as a tool to model games with both sequential and simultaneous moves and to integrate the ideas from the first and second halves of the course.
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Source: https://www.youtube.com/watch?v=D7aDIZ-KPEU
Page title: 18. Imperfect information: information sets and sub-game perfection - YouTube
Meta description: Game Theory (ECON 159)We consider games that have both simultaneous and sequential components, combining ideas from before and after the midterm. We represen...