8. Level-k & Cognitive Hierachy Models Flashcards
Which type of models of strategic thinking do we focus on in this section?
-Focus on applications where players have no precedents with analogous situations (1st round play of game in experiment with inexperienced subjects).
-initial focus on setting where canonical model of strategic thinking only relies on rationality and iterated knowledge of rationality
Describe the P- beauty contest game. Nagel (1995), Ho Et al (1998)
-n subjects make simultaneous guesses between 0-100
-target is p times group average
-if guess= target then prize is won
What is the standard game theoretic prediction of the P-beauty contest?
When p<1 everyone chooses 0. When p>1 everyone chooses 100
What does data from p-beauty test show?
-subjects never play equilibrium strategy initially
-but they also don’t play 1-step dominated choices often
-spikes observed in both treatments (e.g at 50 when p=0.5)
-some people do still choose above 50
What does the boundedly rational reasoning model predict in the P-beauty contest?
Spikes around 25,12.5,6.25 etc and in the limit 0
Results of Bosch-Domenech Et al 2002
In p-beauty contest in newspapers p=2/3
-Financial Times (1,468 subjects), mean=18.91, winning number=13
-Expansion (3,696 subjects), mean=25.47, winning number 16.99
What does Ho Et al 1998 find?
By introducing a reasoning model he finds people converge very rapidly to 0 when p=0.7. So there is learning (with feedback after rounds I assume)
Who coined level-k reasoning?
Stahl(1994,1995)
Ho Et al (1998)
How does a level 2 type play in level-k reasoning?
L(2) type assumes all others are L(1) and chooses a BR to this
Describe the hide and seek game. Rubinstein, Tversky & Heller (1996); Rubinstein (1999)
-4 boxes labelled A B A A
-hider must hide a prize in one of the boxes
-seeker must find prize
-if seeker finds prize they get payoff of 1, if seeker doesn’t find it then hider gets payoff of 1. 0 otherwise
What is the strategy of a fully rational player and L0 player in hide & seek game?
Mixing strategies with prob=1/4 is NE
If L0 is uniformly random then this is the same as NE
Results of Hide and seek game
Most people choose central A followed by B. The outside A’s are picked least by hiders and seekers
What do Crawford & Iriberri 2007 do in the hide and seek game?
They make L0 responsive to salience so there is more weight on B and the endpoints. This fits the data better
Limits of level-k model
-aggregate behaviour fully determined by specification of L0 and by distribution of types
-potential arbitrariness of setting L0
-somewhat concerning that level-k isn’t more accurate than level-k-1 in forming beliefs about others responses
-some issues in predicting outcomes (Crawford Et al 2013)
Describe the cognitive hierarchy model. Camerer, Ho & Chang (2004)
-closely related to level-k but Lk best responds to not only Lk-1 but to a mixture of lower types
-the type frequencies are derived from a parameter used passion distribution
-L0 non strategic and chooses from uniform randomisation
-Lk belief about proportion of Lh players gk(h) with gk(h)=0 for any h>=k+1 and gk(k)=0
What does tau characterise in the poisson distribution?
Mean and variance
What is the desirable property of Poisson distribution?
f(k)/f(k-1) declines with k, so as k rises, thinking beyond k becomes harder so few people do it
What is the median value of tau across estimates?
1.55
Does QRE include strategic thinking, best response, and mutual consistency?
It includes strategic thinking and mutual consistency
Does level-k and cognitive hierarchy model include strategic thinking, best response, and mutual consistency?
It includes strategic thinking and best response
What is behavioural economic theory?
It is the interactive process between data and their theoretical explanation
