a general model of boundedly rational observational
TRANSCRIPT
A General Model ofBoundedly Rational Observational Learning:
Theory and Evidence
Claudia Neri (University of St.Gallen)and
Manuel Mueller-Frank (IESE)
International Meeting on Experimental and Behavioral Social SciencesIMEBESS
April 14, 2016
Motivation
social learning: we learn from others, in many ways!
observational learning: we make inferences on the information that others hold,based on the observation of their behavior
economists ask:
how do individuals behave after observing the behavior of others?
what are the long-run aggregate outcomes?
policy makers ask:
how effective is social advertising? (Mueller-Frank & Pai 2015)how effective is a microfinance information campaign? (Banerjee et al. 2013)etc
Mueller-Frank and Neri Boundedly Rational Observational Learning 1 / 21
Motivation
social learning: we learn from others, in many ways!
observational learning: we make inferences on the information that others hold,based on the observation of their behavior
economists ask:
how do individuals behave after observing the behavior of others?
what are the long-run aggregate outcomes?
policy makers ask:
how effective is social advertising? (Mueller-Frank & Pai 2015)how effective is a microfinance information campaign? (Banerjee et al. 2013)etc
Mueller-Frank and Neri Boundedly Rational Observational Learning 1 / 21
Motivation
social learning: we learn from others, in many ways!
observational learning: we make inferences on the information that others hold,based on the observation of their behavior
economists ask:
how do individuals behave after observing the behavior of others?
what are the long-run aggregate outcomes?
policy makers ask:
how effective is social advertising? (Mueller-Frank & Pai 2015)how effective is a microfinance information campaign? (Banerjee et al. 2013)etc
Mueller-Frank and Neri Boundedly Rational Observational Learning 1 / 21
Motivation
social learning: we learn from others, in many ways!
observational learning: we make inferences on the information that others hold,based on the observation of their behavior
economists ask:
how do individuals behave after observing the behavior of others?
what are the long-run aggregate outcomes?
policy makers ask:
how effective is social advertising? (Mueller-Frank & Pai 2015)how effective is a microfinance information campaign? (Banerjee et al. 2013)etc
Mueller-Frank and Neri Boundedly Rational Observational Learning 1 / 21
Motivation
social learning: we learn from others, in many ways!
observational learning: we make inferences on the information that others hold,based on the observation of their behavior
economists ask:
how do individuals behave after observing the behavior of others?
what are the long-run aggregate outcomes?
policy makers ask:
how effective is social advertising? (Mueller-Frank & Pai 2015)how effective is a microfinance information campaign? (Banerjee et al. 2013)etc
Mueller-Frank and Neri Boundedly Rational Observational Learning 1 / 21
Motivation (cont.)
Modeling observational learning:
repeated decision-making under uncertainty
individuals observe their own private information
individuals observe the choices of others
Two approaches:
Bayesian updating:
Bikhchandani, Hirshleifer & Welch 1992; Banerjee 1992; Smith & Sorensen2000; Gale & Kariv 2003; ....individuals learn rationally: they make inferences on the private informationof all agents based on the interaction structure and the observed actionspros: useful benchmark
cons: unrealistic, requires computational sophistication
Boundedly rational updating:
DeGroot 1973; DeMarzo, Vayanos & Zwiebel 2003; Golub & Jackson2010&2012; Acemoglu, Ozdaglar & ParandehGheibi 2010pros: tractablecons: arbitrary, requires an infinite real-numbered action space
Mueller-Frank and Neri Boundedly Rational Observational Learning 2 / 21
Motivation (cont.)
Modeling observational learning:
repeated decision-making under uncertainty
individuals observe their own private information
individuals observe the choices of others
Two approaches:
Bayesian updating:
Bikhchandani, Hirshleifer & Welch 1992; Banerjee 1992; Smith & Sorensen2000; Gale & Kariv 2003; ....individuals learn rationally: they make inferences on the private informationof all agents based on the interaction structure and the observed actionspros: useful benchmark
cons: unrealistic, requires computational sophistication
Boundedly rational updating:
DeGroot 1973; DeMarzo, Vayanos & Zwiebel 2003; Golub & Jackson2010&2012; Acemoglu, Ozdaglar & ParandehGheibi 2010pros: tractablecons: arbitrary, requires an infinite real-numbered action space
Mueller-Frank and Neri Boundedly Rational Observational Learning 2 / 21
Motivation (cont.)
Modeling observational learning:
repeated decision-making under uncertainty
individuals observe their own private information
individuals observe the choices of others
Two approaches:
Bayesian updating:
Bikhchandani, Hirshleifer & Welch 1992; Banerjee 1992; Smith & Sorensen2000; Gale & Kariv 2003; ....individuals learn rationally: they make inferences on the private informationof all agents based on the interaction structure and the observed actions
pros: useful benchmark
cons: unrealistic, requires computational sophistication
Boundedly rational updating:
DeGroot 1973; DeMarzo, Vayanos & Zwiebel 2003; Golub & Jackson2010&2012; Acemoglu, Ozdaglar & ParandehGheibi 2010pros: tractablecons: arbitrary, requires an infinite real-numbered action space
Mueller-Frank and Neri Boundedly Rational Observational Learning 2 / 21
Motivation (cont.)
Modeling observational learning:
repeated decision-making under uncertainty
individuals observe their own private information
individuals observe the choices of others
Two approaches:
Bayesian updating:
Bikhchandani, Hirshleifer & Welch 1992; Banerjee 1992; Smith & Sorensen2000; Gale & Kariv 2003; ....individuals learn rationally: they make inferences on the private informationof all agents based on the interaction structure and the observed actionspros: useful benchmark
cons: unrealistic, requires computational sophistication
Boundedly rational updating:
DeGroot 1973; DeMarzo, Vayanos & Zwiebel 2003; Golub & Jackson2010&2012; Acemoglu, Ozdaglar & ParandehGheibi 2010pros: tractablecons: arbitrary, requires an infinite real-numbered action space
Mueller-Frank and Neri Boundedly Rational Observational Learning 2 / 21
Motivation (cont.)
Modeling observational learning:
repeated decision-making under uncertainty
individuals observe their own private information
individuals observe the choices of others
Two approaches:
Bayesian updating:
Bikhchandani, Hirshleifer & Welch 1992; Banerjee 1992; Smith & Sorensen2000; Gale & Kariv 2003; ....individuals learn rationally: they make inferences on the private informationof all agents based on the interaction structure and the observed actionspros: useful benchmark
cons: unrealistic, requires computational sophistication
Boundedly rational updating:
DeGroot 1973; DeMarzo, Vayanos & Zwiebel 2003; Golub & Jackson2010&2012; Acemoglu, Ozdaglar & ParandehGheibi 2010pros: tractablecons: arbitrary, requires an infinite real-numbered action space
Mueller-Frank and Neri Boundedly Rational Observational Learning 2 / 21
Motivation (cont.)
Modeling observational learning:
repeated decision-making under uncertainty
individuals observe their own private information
individuals observe the choices of others
Two approaches:
Bayesian updating:
Bikhchandani, Hirshleifer & Welch 1992; Banerjee 1992; Smith & Sorensen2000; Gale & Kariv 2003; ....individuals learn rationally: they make inferences on the private informationof all agents based on the interaction structure and the observed actionspros: useful benchmark
cons: unrealistic, requires computational sophistication
Boundedly rational updating:
DeGroot 1973; DeMarzo, Vayanos & Zwiebel 2003; Golub & Jackson2010&2012; Acemoglu, Ozdaglar & ParandehGheibi 2010
pros: tractablecons: arbitrary, requires an infinite real-numbered action space
Mueller-Frank and Neri Boundedly Rational Observational Learning 2 / 21
Motivation (cont.)
Modeling observational learning:
repeated decision-making under uncertainty
individuals observe their own private information
individuals observe the choices of others
Two approaches:
Bayesian updating:
Bikhchandani, Hirshleifer & Welch 1992; Banerjee 1992; Smith & Sorensen2000; Gale & Kariv 2003; ....individuals learn rationally: they make inferences on the private informationof all agents based on the interaction structure and the observed actionspros: useful benchmark
cons: unrealistic, requires computational sophistication
Boundedly rational updating:
DeGroot 1973; DeMarzo, Vayanos & Zwiebel 2003; Golub & Jackson2010&2012; Acemoglu, Ozdaglar & ParandehGheibi 2010pros: tractablecons: arbitrary, requires an infinite real-numbered action space
Mueller-Frank and Neri Boundedly Rational Observational Learning 2 / 21
What we do
we propose a general model of boundedly rational observational learning, based onthe concept of Quasi-Bayesian updating
reduced complexity compared to Bayesian updating:not necessary to consider how each observed action might have been affectedby other actionsrationally foundednot arbitraryapplicable to any environment: no restriction on utility function, state space,action space or signal space
we provide experimental evidence on Quasi-Bayesian updating
Mueller-Frank and Neri Boundedly Rational Observational Learning 3 / 21
What we do (cont.)
we apply Quasi-Bayesian updating to a model of repeated interaction in socialnetworks with binary actions
consensus and information aggregation
generally coincidehard to achieve, since they require highly asymmetric environmentsachievable in finite networks, not in infinite networks
we provide experimental evidence on consensus and information aggregation
Mueller-Frank and Neri Boundedly Rational Observational Learning 4 / 21
The ModelObservational learning
Simplified setting (general setting in the paper):
finite set of agents
binary states, binary actions, binary signals Ω = A = S = 0, 1agents share a common prior over the state space Ω
each agent observes an iid private signal from the signal space S
the distribution over the signal space depends on the realized state
utility = 1 if chosen action matches the realized state, = 0 otherwise
each agent chooses an EU-maximizing action from the action space A
each agent observes a subset of other agents and the actions they chose, andupdates his own action
Mueller-Frank and Neri Boundedly Rational Observational Learning 5 / 21
The ModelQuasi-Bayesian updating
Quasi-Bayesian updatingChoosing an action which is Bayes-optimal conditional on the observed actionsassuming that each observed action was selected by the corresponding agent based onlyon his private signal.
in other models of observational learning:... based also on information inferred from the actions chosen by others
Quasi-Bayesian updating abstracts away from:
structure of interactionindirect inferences on the private information of all agents
Mueller-Frank and Neri Boundedly Rational Observational Learning 6 / 21
The ModelQuasi-Bayesian updating
its specific functional form and its general properties vary among environments
we analyze its implications for aggregate behavior in a model of repeatedinteraction in social networks
Mueller-Frank and Neri Boundedly Rational Observational Learning 7 / 21
The ModelQuasi-Bayesian updating and repeated interaction in social networks
finite set of agents organized in a strongly connected network
agents face uncertainty as described in the general model
t = 0: the state is drawn
t = 1: each agent observes a private signal, and then chooses an action
t = 2, 3, ..: each agent observes the action chosen by each of his neighbors int − 1, and then updates his action
Mueller-Frank and Neri Boundedly Rational Observational Learning 8 / 21
The ModelQuasi-Bayesian updating and repeated interaction in social networks
Under which conditions do consensus and information aggregation occur?
consensusconvergence to agreement on one action(for any strongly connected network, for any initial action profile)
information aggregationconsensus on an optimal action conditional on the initial action profile(for any strongly connected network, for any initial action profile)
Mueller-Frank and Neri Boundedly Rational Observational Learning 9 / 21
The ModelQuasi-Bayesian updating and repeated interaction in social networks
Under Quasi-Bayesian updating, assuming binary actions:
Theorem 1: consensusnecessary and sufficient condition: highly asymmetric environment:one action is optimal conditional on every possible profile of observed actions, except forthe profile where all agents choose the other action
Theorem 2: information aggregationnecessary and sufficient condition: same as in Theorem 1
Theorem 3for every environment there exists a finite network size n∗ such that consensus andinformation aggregation fail for all networks of size larger than n∗
Mueller-Frank and Neri Boundedly Rational Observational Learning 10 / 21
The ModelQuasi-Bayesian updating and repeated interaction in social networks
Under Quasi-Bayesian updating, assuming binary actions:
Theorem 1: consensusnecessary and sufficient condition: highly asymmetric environment:one action is optimal conditional on every possible profile of observed actions, except forthe profile where all agents choose the other action
Theorem 2: information aggregationnecessary and sufficient condition: same as in Theorem 1
Theorem 3for every environment there exists a finite network size n∗ such that consensus andinformation aggregation fail for all networks of size larger than n∗
Mueller-Frank and Neri Boundedly Rational Observational Learning 10 / 21
The ModelQuasi-Bayesian updating and repeated interaction in social networks
Under Quasi-Bayesian updating, assuming binary actions:
Theorem 1: consensusnecessary and sufficient condition: highly asymmetric environment:one action is optimal conditional on every possible profile of observed actions, except forthe profile where all agents choose the other action
Theorem 2: information aggregationnecessary and sufficient condition: same as in Theorem 1
Theorem 3for every environment there exists a finite network size n∗ such that consensus andinformation aggregation fail for all networks of size larger than n∗
Mueller-Frank and Neri Boundedly Rational Observational Learning 10 / 21
The ModelQuasi-Bayesian updating and repeated interaction in social networks
Consensus and information aggregation
with Quasi-Bayesian in the DeGroot modelupdating & its generalizations
achievable only in achievable only infinite networks infinite networks
hard to achieve easy to achieve
Mueller-Frank and Neri Boundedly Rational Observational Learning 11 / 21
The experimentTask, matching and treatments
urn-guessing game (Anderson&Holt 1997;Choi,Gale&Kariv 2005;Grimm&Mengel 2015)
198 participants
fixed-group random matching
subjects are assigned with a label-identity (A, B, C, ...)subjects are matched into groups (each with a different label-identity)
treatments:
network size (within-subject): 5- or 7-agent networksnetwork connections (between-subject): 1-4 neighbors for each subjectchoice set (between-subject): 2 or 4 urns
rounds correspond to between-subject treatments
each round consists of turns, when choices can be updated
network size subjects groups rounds turns obs.per round
5 100 20 18 6 108007 98 14 14 8 10976all 198 34 21776
Mueller-Frank and Neri Boundedly Rational Observational Learning 12 / 21
The experimentUrn-guessing game
Figure : 2-urn game
black urnwhite urn
Figure : 4-urn game
red urn yellow urn
green urn blue urn
Mueller-Frank and Neri Boundedly Rational Observational Learning 13 / 21
The experimentTiming
each subject privately
observes a ball drawn
randomly from the urn
1st decision turn: “what urn is
used?”
each subject observes the
previous choices of his
neighbors
round
the computer randomly
selects one urn
next round
2nd decision turn: “what urn is
used?”
last decision turn: “what urn is
used?”
Mueller-Frank and Neri Boundedly Rational Observational Learning 14 / 21
The experimentNetwork structure
Since the theoretical framework holds “for any network structure”,the experiment implements several network structures
Figure : 5-agent networks
B
A
C D
E
complete
B
A
C D
E
linked circle A-‐C
B
A
C D
E
linked circle A-‐D
B
A
C D
E
linked circle B-‐D
B
A
C D
E
linked circle B-‐E
B
A
C D
E
linked circle C-‐E
B
A
C D
E
star (A center)
B
A
C D
E
star (B center)
B
A
C D
E
star (C center)
Mueller-Frank and Neri Boundedly Rational Observational Learning 15 / 21
The experimentNetwork structure
Since the theoretical framework holds “for any network structure”,the experiment implements several network structures
Figure : 7-agent networks
B
A
C
D E
F
G
small world 1: A-‐C, D-‐F
B
A
C
D E
F
G
small world 2: B-‐D, E-‐G
B
A
C
D E
F
G
small world 3: C-‐E, F-‐A
B
A
C
D E
F
G
small world 4: A-‐D, B-‐G
B
A
C
D E
F
G
small world 5: A-‐D
B
A
C
D E
F
G
small world 6: A-‐D, A-‐E, B-‐G
B
A
C
D
E
F
G
connected complete components
Mueller-Frank and Neri Boundedly Rational Observational Learning 15 / 21
The experimentNetwork structure
Since the theoretical framework lifts the assumption of (common) knowledge of thenetwork structure, the experiment implements no knowledge of the network structure
each subject knows how many neighbors he has and what their label-identity is,
but ignores how many neighbors other members of the network have
Mueller-Frank and Neri Boundedly Rational Observational Learning 16 / 21
Results1st-turn choices
In the 1st turn subjects choose an action based on their private signal.
24 THE AMERICAN ECONOMIC REVIEW MONTH YEAR
lected round was correct.41 Otherwise they received nothing. Participants’
earnings ranged between CHF 22 and CHF 42.5, with an average of CHF
34 (including a CHF 10 show-up fee).42
IV. Experimental evidence: Quasi-Bayesian updating
In this section we analyze the experimental data in the light of the the-
oretical framework presented in Section II. We begin by describing agents’
behavior in the first round. As one might expect, in the first round agents
choose an action based on their private signal. Table 2 reports the distri-
bution across individuals of the frequency with which first-round choices
coincide with private signals. The mean is 0.97 in 5-agent networks and
0.95 in 7-agent networks, and the median is 1 for both network sizes.
Table 2—: Frequency of 1st-round choice equal to private signal. Distribu-tion across individuals.
obs mean median std5-agent networks
all games 100 0.97 1 0.102-urn games 100 0.97 1 0.114-urn games 100 0.97 1 0.127-agent networks
all games 98 0.95 1 0.132-urn games 98 0.94 1 0.144-urn games 98 0.96 1 0.13
We then inspect agents’ behavior in rounds following the first, when agents
have the opportunity to revise their choice after observing their neighbors’
41The difference in payment per correct-decision (CHF 2 versus CHF 2.5) was gaugedto attain similar expected earnings for subjects irrespective of the session they partici-pated in, in order to comply with the ETH Decision Science Lab rules.
42In sessions with 5-subject networks, the range was CHF 22-42 (average CHF 35). Insessions with 7-subject networks, the range was CHF 22.5-42.5 (average CHF 33).
Figure : Empirical distribution of the frequency of 1st-turn choice coinciding with private signal.
Mueller-Frank and Neri Boundedly Rational Observational Learning 17 / 21
ResultsQuasi-Bayesian updating
Pool all data
5-agent networks 7-agent networksstar linked complete linked connected
circle circle complete2-urn 0.95 0.92 0.91 0.91 0.90
4-urn 0.94 0.90 0.90 0.89 0.91
Table : Percentage of choices consistent with Quasi-Bayesian updating (t = 2, 3, ..).
Mueller-Frank and Neri Boundedly Rational Observational Learning 18 / 21
ResultsQuasi-Bayesian updating
Define for each subject the fraction of choices consistent with Quasi-Bayesian updating.26 THE AMERICAN ECONOMIC REVIEW MONTH YEAR
0.2
.4.6
Frac
tion
0 .2 .4 .6 .8 1Quasi-Bayesian updating (individual score)
(a) 2-urn games, 5-agent networks
0.2
.4.6
Frac
tion
0 .2 .4 .6 .8 1Quasi-Bayesian updating (individual score)
(b) 2-urn games, 7-agent networks
0.2
.4.6
Frac
tion
0 .2 .4 .6 .8 1Quasi-Bayesian updating (individual score)
(c) 4-urn games, 5-agent networks
0.2
.4.6
Frac
tion
0 .2 .4 .6 .8 1Quasi-Bayesian updating (individual score)
(d) 4-urn games, 7-agent networks
Figure 1. : Empirical distribution of participants’ individual consistencywith Quasi-Bayesian updating. A kernel density estimate is also reported,using an Epanechnikov kernel function with optimal half-width.
V. Long-run properties of Quasi-Bayesian updating in social
networks
The two main questions addressed by the literature on learning in so-
cial networks concern the conditions on the environment and the network
structure under which consensus (i.e. asymptotic agreement in actions)
and information aggregation (i.e. optimality of long-run actions conditional
on the pooled private information of all agents) occur.44 We address both
44For an analysis of consensus see DeMarzo, Vayanos and Zwiebel (2003) and Mueller-Frank (2014) for non-Bayesian models, and Gale and Kariv (2003), Rosenberg, Solanand Vieille (2009), and Mueller-Frank (2013a) for Bayesian models. For an analysis oflearning see Golub and Jackson (2010), Mueller-Frank (2013a,2014), Arieli and Mueller-
Figure : Distribution of participants’ individual consistency with Quasi-Bayesian updating. Median > 92%.
Mueller-Frank and Neri Boundedly Rational Observational Learning 19 / 21
ResultsConsensus and information aggregation
Fraction of groups reaching consensus by the last updating turn.
5-agent networks 7-agent networksstar linked complete linked connected
circle circle complete
consensus 0.48 0.59 0.70 0.29 0.50
of whichwith information 0.97 0.98 1 0.96 1aggregation
Table : Two-urn games. Averages across 20 groups for 5-agent networks and across 14 groups for 7-agent networks.
Mueller-Frank and Neri Boundedly Rational Observational Learning 20 / 21
What we did and what is next
what we did
general model of boundedly rational observational learning based on the concept ofQuasi-Bayesian updating
conditions under which Quasi-Bayesian updating yields consensus and informationaggregation in a model of repeated interaction in social networks
support from experimental evidence:
Quasi-Bayesian updatingconsensus is hard to achieveif consensus occurs, it achieves information aggregation
what is nextIs Quasi-Bayesian updating a good description of behavior in other observationallearning environments and in more complex settings?
Mueller-Frank and Neri Boundedly Rational Observational Learning 21 / 21