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
