Understanding the 2/3 Average Game

The video introduces a guessing game challenge where participants guess a number closest to 2/3 of the average of all guesses. It explores the concept of common knowledge in game theory, where players have the same information and know others do too. The video discusses real-world outcomes, showing that people often don't act perfectly rationally. It introduces k-level reasoning, a model for understanding decision-making, and its applications in fields like stock trading and soccer. The video concludes by inviting viewers to participate in the game and consider the difference between logical and common approaches.

What is the main objective of the 2/3 average guessing game?

• To guess the highest number possible

• To guess a number randomly

• To guess the exact average of all guesses

• To guess the number closest to 2/3 of the average of all guesses

In the context of the game, what does 'common knowledge' imply?

• Only a few players have the necessary information

• Every player has different information

• Players are unaware of the rules

• All players have the same information and know that others do too

What is the Nash Equilibrium in the context of this game?

• A state where players guess based on others' guesses

• A state where players choose numbers randomly

• A state where every player chooses the highest number

• A state where no player can benefit by changing their guess

Why do real-world results of the game differ from the logical outcome?

• Players always choose zero

• Players are perfectly rational

• Players expect others to be perfectly rational

• Players are not perfectly rational or expect others not to be

What does k-level reasoning involve?

• Guessing without any strategy

• Ignoring other players' strategies

• Repeating cycles of reasoning about others' guesses

• Choosing the highest possible number

At k-level 1, what assumption does a player make?

• Everyone else is playing at k-level 0

• Everyone else is playing at k-level 2

• Everyone else is playing at k-level 3

• Everyone else is playing at k-level 1

How is k-level reasoning applied in stock trading?

• Traders only consider their own analysis

• Traders ignore others' valuations

• Traders consider both earnings reports and others' valuations

• Traders always follow market trends

In soccer penalty kicks, how do players use k-level reasoning?

• Players always kick to the left

• Players ignore the goalie's patterns

• Players decide based on their own preferences

• Players anticipate the opponent's thoughts and actions

What might happen if players understand the difference between logical and common approaches in the game?

• They might adjust their expectations and strategies

• They will always choose the highest number

• They will always choose zero

• They will ignore the game's rules

What is the purpose of inviting participants to submit their guesses after understanding the game?

• To ensure everyone chooses zero

• To encourage random guessing

• To evaluate their understanding of the logical approach

• To see if they choose the highest number