Game Theory | Information | Incomplete Information Concepts | Introduction|

Summary

This video explores the concepts of asymmetric and incomplete information in game theory, using real-life scenarios like house buying and used car sales. It explains how players often have private information that others don’t, creating uncertainty and affecting decision-making. The transcript highlights key ideas such as the concept of 'types' (player preferences and valuations), the role of 'moves of nature' (random decisions based on probabilities), and how these factors lead to more complex and realistic games. It emphasizes that in such games, not all participants know everything about others' preferences or intentions.

Takeaways

• 😀 Players in a game with imperfect information don't know everything about other participants, leading to an asymmetry in the available information.
• 😀 Private information is when a player knows something that others don’t, creating an information gap between participants.
• 😀 Asymmetric information occurs when one player has more or better information than others, such as a buyer knowing their willingness to pay while the seller does not.
• 😀 Nature is imagined as 'Player Zero' in game theory, making random moves at the start of the game, such as determining the true value of a house in a sale.
• 😀 The moves of nature are random, non-strategic, and drawn from known probability distributions, meaning nature is not trying to maximize profit or win.
• 😀 In a game with incomplete information, some players don’t know what others know or prefer, which creates uncertainty and adds complexity to decision-making.
• 😀 The concept of 'type' refers to a player’s private information, such as their maximum willingness to pay, which is known only to them, but not to other players.
• 😀 A seller does not know the buyer's true willingness to pay, but may have some probabilistic guesses based on observable characteristics like income.
• 😀 In the house-buying game, the buyer knows their maximum willingness to pay, but the seller only has a belief about what that value could be based on probabilities.
• 😀 Incomplete information in games arises from asymmetric information, often caused by the moves of nature, creating uncertainty in player interactions and decisions.

Q & A

What is meant by 'asymmetric information' in game theory?

Asymmetric information refers to a situation where one player knows something that others do not. This creates an imbalance of knowledge between participants in the game.

Can you explain the role of 'nature' in game theory?

In game theory, nature is considered a non-strategic player (denoted as Player Zero) that introduces randomness at the beginning of the game. Nature's moves are random and are based on known probabilities, not aiming to maximize profit or win.

What is 'private information' in the context of game theory?

Private information exists when one player knows something that others do not. For example, a buyer might know their maximum willingness to pay for an item, but the seller does not.

What makes games of incomplete information more realistic?

Games of incomplete information are more realistic because, in real life, players often do not know everything about the other participants. This leads to uncertainty and makes decision-making more complex.

What is the difference between perfect and imperfect information games?

Perfect information games are those where all players know everything about the game, including the actions and preferences of others. In contrast, imperfect information games involve uncertainty, where some players don't know everything about others' preferences or knowledge.

How does 'belief' play a role in games of asymmetric information?

In games of asymmetric information, players form beliefs about others' private information. For example, a seller may not know a buyer's exact willingness to pay but may have beliefs or guesses based on probabilities about the buyer's preferences.

What does the concept of 'type' refer to in game theory?

The concept of 'type' refers to a player's private information, such as their preferences, valuation, or costs. Each player knows their own type, but other players may not.

How does nature's random move affect the game in a scenario like buying a house?

Nature’s random move determines the true value of the house in the buyer's mind, such as whether they value it at $100,000 or $200,000. This randomness introduces uncertainty into the game, as the seller only knows the probabilities of these outcomes, not the exact value.

Why can't a seller know the exact willingness to pay of a buyer?

The seller cannot know the exact willingness to pay of a buyer because the buyer's valuation is private information. The buyer knows their own willingness to pay, but the seller only has beliefs or probabilities about the buyer's potential value.

What is meant by 'incomplete information' in game theory?

Incomplete information in game theory refers to a situation where players do not know everything about others' preferences, costs, or private information. This uncertainty arises due to asymmetric information, often caused by nature's random moves.