Nagel: Unravelling in Guessing Games Flashcards
(17 cards)
What is a p-beauty contest game?
A game where players choose numbers between 0-100, and the winner is the player whose number is closest to p times the average of all numbers chosen (typically p=2/3)
What is the NE in a p-beauty contest where p < 1?
Zero. Through infinite iterations of reasoning, the only stable solution is for all players to choose 0.
What does “unravelling” refer to in the context of guessing games?
The iterative process of strategic reasoning that should theoretically lead players toward the eqm.
What is bounded rationality?
The concept that human decision making is limited by cognitive capacity, available information, and time constraints, causing people to “satisfice” rather than optimise.
In Nagel’s research, how many steps of iterative reasoning do most players demonstrate?
Most players exhibit 1-2 steps of reasoning (Level 1 and Level 2), with very few demonstrating Level 3 or higher thinking.
How does Nagel’s Second Model treat Order-0 players differently from the First Model?
The Second Model allows for multiple types of Order-0 behaviour beyond just randomness, including focal points and other heuristics, rather than simply assuming a uniform distribution.
What defines an Order 1 thinker in the p-beauty contest?
A player who assumes others choose randomly (averaging around 50) and therefore selects p x 50
What defines an Order 2 thinker in the p beauty contest?
A player who assumes others are Order 1 thinkers and therefore selects p^2 x 50
What is partial reasoning or “order p” in Nagel’s Second Model?
Incomplete iterative reasoning where players begin the reasoning where players begin the reasoning process, but stop becore reaching a natural conclusion
What is iterated deletion of dominated strategies?
A solution concept where strategies that are strictly worse than others are progressively eliminated, with new domination relationships emerging after each round of elimination.
What is the difference between best response dynamics and iterated elimination?
Best response dynamics focuses on optimal reactions to beliefs about others’ play, while iterated elimination systematically removes irrational choices before forming beliefs.
What typical pattern emerges in first-round p-beauty contest games?
Most choices cluster around the values corresponding to Level-1 (33.33) and Level-2 (22.22) thinking, with very few at equilibrium (0).
What evidence supports the presence of anticipatory learning in multi-round p-beauty contests?
Some players “leapfrog” beyond what simple best response would predict, suggesting they anticipate that others are also learning and adjusting downward.
What statistical methods can identify different behavioral types in p-beauty contest data?
Mixture models, strategy classification based on proximity to theoretical predictions, process tracing methods, and analysis of individual consistency across rounds.
Do any players actually expect a Nash equilibrium in initial rounds?
Experimental evidence suggests very few do, as almost no players choose 0 or values extremely close to it in initial rounds.
How relevant is iterated reasoning in later rounds of repeated p-beauty contests?
Its relevance appears to diminish as empirical evidence from previous rounds provides direct guidance, with players shifting toward pattern recognition and experience based learning.
