When it Pays to be Neurotic or to Have Blind Spots:
The Value of Understanding External
and Internal Contingencies
Dirk Martignoni, University of St. Gallen
Nicolaj Siggelkow, Wharton School
Motivation
•
Contingency relationships are prevalent in organizational life
•
The value of many activities is affected by
–
–
•
External factors (environmental turbulence, complexity, weather, exchange rate)
(classic contingency literature, Lawrence & Lorsch (1967))
Internal factors (other activity choices) (complementarity/activity system literature,
Milgrom & Roberts (1990), Porter (1996))
While many contingencies appear intuitive, it has been quite hard to pin
them down empirically (Athey & Stern 1998; Ichniowski et al. 1997)
–
Long time frames, lot’s of data, sophisticated econometrics, precise measures etc.
•
As a result, it is quite likely that managers operate with mental models that
do not accurately reflect all contingency relationships that affect the choices
they control
•
If that’s true, then a range of questions arises…
Research Questions
•
How valuable is a precise understanding of contingency
relationships?
•
What are the costs of having a mental model that is overspecified
or “neurotic,” i.e., assumes interdependencies that actually do not
exist?
•
What are the costs of having a mental model that is underspecified
or “blind” to interactions that actually do exist?
•
Under which conditions are these errors particularly costly?
•
Is it always optimal to have a correct mental model?
 We build a simulation model to make some headway on these
questions
Simple Example
•
Assume a manager contemplates how to best promote a new
product
– She has three alternatives: run a TV ad; put an ad in a magazine; distribute
flyers on the street
– For a new product, the values of these alternatives are unknown to the
manager
•
The manager may run some experiments to estimate the values of
her alternatives
– The signals she receives about her alternatives’ values are noisy.
•
•
Now, assume that there is an external (contingency) factor such as
“weather”
The manager might believe that certain contingency relationships
exist, i.e., that the value of her alternatives depend on the weather
conditions
Mental Model and Mental Map
•
•
•
Mental model: The manager’s beliefs about what contingency
relationships exist
Mental map: The manager’s beliefs about the expected payoffs of
actions given a specific contingency
Mental models answer questions such as:
– Do I believe that the effectiveness of TV ads is influenced by
the weather?
•
Yes No
Mental maps answer questions such as:
– When it rains, what is the expected benefit of a TV ad?
– When the sun shines, what is the expected benefit of a TV ad?
a
b
c
c
Misspecified Mental Models
•
A mental model may be correct or incorrect
– We look at two types of misspecifications: under- and overspecification. The
manager may ignore contingency relationships (i.e., have blind spots) or
assume contingency relationships where there are actually none (i.e. be
neurotic)
•
With internal contingencies, replace “external contingency” with
“other choice” (“staffing level of call center”). Now, however, both
choices are under her control, and she will have two mental maps
(and models), one for each choice
Conventional Wisdom
•
Prior research has generated evidence for both types of imperfections
(having blind spots and being neurotic)
–
–
–
•
Simplified mental models: Bettis and Prahalad (1995), Porac et al. (1995), Walsh
(1995)
Superstitious learning: Levitt and March (1991), Denrell, Fang, Levinthal (2004)
Gary and Wood (2008): experimental study showing that both types arise
Few empirical studies on cost of misspecification. Generally, models that
are more complex are better, but models that are too complex can also
come at a cost.
Proposition: It is more valuable to have the correct mental model
than to have a mental model that is overspecified or
underspecified
•
We will use our model to identify possible boundary conditions to this
conventional wisdom
Simulation Overview
Mental
map
Manager
observes
external
contingency
Guided by
mental map,
manager
chooses an
alternative
Performance
landscape
Manager observes the
performance of the
chosen alternative;
performance is affected
by the true
performance landscape
Mental
model
Guided by
mental
model,
manager
updates
mental map
Elements of the Model
•
•
•
•
•
Performance landscape
Mental model
Mental map
Updating the mental map
Choosing alternatives
Elements of the Model: Performance Landscape
5
2.1
-2.7
3.3
-1.7
1.1
4
2.1
-2.7
3.3
-1.7
1.1
3
2.1
-2.7
3.3
-1.7
1.1
2
2.1
-2.7
3.3
-1.7
1.1
1
2.1
-2.7
3.3
-1.7
1.1
2
3
4
Choice Alternatives
5
1
•
•
•
•
High Complexity (p=0.48)
Contingency States
Contingency States
Low Complexity (p=0)
5
3.4
-2.7
3.3
-1.7
5.8
4
2.1
1.1
3.3
4.0
1.1
3
-2.1
-2.7
3.3
-1.7
1.1
2
4.5
2.0
3.3
5.6
1.1
1
-1.9
-1.8
2.2
-1.7
-4.3
1
2
3
4
Choice Alternatives
5
Realized performance of (state = r, choice = c) ~ N(mrc, 1)
In the case of no complexity (no interdependency) (p=0), all entries
along a column are identical
Mean values, mrc , are drawn from N(0,1)
In the case of complexity p>0, an entry is replaced by a new draw
from N(0,1) with probability p (right panel, bold black borders)
Elements of the Model: Mental Map
Mental map is also a Contingency x Alternative matrix
– Each cell contains the belief about the value of a choice/contingency
combination
– At t = 0, it contains all 0’s (i.e., correct on average but no strong priors)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Choice Alternatives
Mental Map at the end
of period t=0
Contingency State
Mental Map at the end
of period t=0
Contingency State
•
1.1
3.2
5.2
3.1
-0.2
0.0
3.7
1.0
-1.2
Choice Alternatives
Elements of the Model: Mental Model
•
Mental model is reflected in the number of cells for which different entries are
allowed (different colors):
– Identical colors= belief about identical values
•
We will often look at three archetypical cases:
– Correctly specified, no-interaction, full-interaction mental model
– Note: a correctly specified model might still contain incorrect estimates
within a cell
No-interaction
Mental Map atmental
the endmodel
of period t=0
Contingency State
Contingency State
of period t=0
Mental Map at
the end
Full-interaction
mental
model
Choice Alternatives
Choice Alternatives
Choosing Alternatives and Updating of Mental Map
0.0
0.0
0.0
2
0.0
0.0
0.0
1
0.0
0.0
0.0
1
2
3
State =3
Choice=1
Payoff 0.6
Choice Alternatives
Contingency State
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Choice Alternatives
0.3
0.0
0.0
2
0.3
0.0
0.0
1
0.3
0.0
0.0
1
2
3
State =2
Choice=1
Payoff -0.9
Choice Alternatives
Mental Map at the end
of period t=0
Fullinteraction
mental
model
3
Mental Map at the end
of period t=2
Payoff 0.6
0.3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Choice Alternatives
-0.1
0.0
0.0
2
-0.1
0.0
0.0
1
-0.1
0.0
0.0
1
2
3
Choice Alternatives
Mental Map at the end
of period t=1
State =3
Choice=1
3
Mental Map at the end
of period t=2
State =2
Choice=2
Payoff -0.9
Contingency State
3
Mental Map at the end
of period t=1
Contingency States
Nointeraction
mental
model
Mental Map at the end
of period t=0
Contingency State
•
Contingency States
•
The manager picks the alternative that she believes will yield highest
performance given the contingency state, which is observable before an action
is taken
If more than one alternative has highest performance, she chooses randomly
among them (with equal probabilities)
Updating: average over all experiences within the relevant group of cells
Contingency States
•
0.3
0.0
0.0
0.0
-0.45
0.0
0.0
0.0
0.0
Choice Alternatives
Parameters
•
•
•
•
Landscapes and mental maps are 5 x 5
Each external contingency has the same probability of occurring in
each period
Run models 200 periods (and show t = 20 and t = 200 results)
Run each model 10,000 times
Short-run Results for External Contingencies
1
no-interaction mental model
correct mental model
full interaction mental model
0.9
Performance in t=20
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0
0.1
0.2
0.3
0.4
0.5
Complexity
0.6
0.7
Prop: correct model is best 
• Underspecification  wrong generalizations
• Overspecification  slow improvement
0.8
0.9
1
Long-run Results for External Contingencies
1
0.9
no-interaction mental model
Performance in t=200
0.8
correct mental model
full interaction mental model
0.7
0.6
0.5
0.4
0
0.1
0.2
0.3
Prop: correct model is best
-
0.4
0.5
Complexity
0.6
0.7
0.8
0.9
1

Performance of full-interaction model is unaffected by complexity (but
both short-run and long-run cost)
Inversely U-shaped performance and benefit of correct mental model
Endogenous Exploration Induced by Complexity
18.5
# Updated Entries in the Mental Model
18
17.5
no-interaction mental model
correct mental model
full interaction mental model
17
16.5
16
15.5
15
14.5
14
13.5
0
•
•
•
0.1
0.2
0.3
0.4
0.5
Complexity
0.6
0.7
0.8
0.9
1
For correct mental models, exploration follows an inversely
U-shaped pattern, similar to the performance-complexity relationship
Full interaction mental models are unaffected by complexity
No-interaction models lead to incorrect updating, i.e. the manager
incorrectly generalizes experiences (opinions  useful exploration)
2.0
4.0
3.0
2.0
4.0
3.0
2.0
4.0
Contingency State
Mental Map at the end
of period t=0
0.0
0.0
0.0
0.0
0.0
0.0
Choice Alternatives
Mental
Map atLandscape
the end
Performance
of period t=1
State =3
Choice=1
0.0
3.0
1.6
2.0
0.0
4.0
0.0
1.0
1.6
2.0
0.0
4.0
0.0
Choice Alternatives
State =x
Choice=1
4.0
3.0
1.0
2.0
4.0
3.0
2.0
Contingency State
Contingency State
2.0
4.0
Choice Alternatives
State
Mental Map at the end
of period t=0
0.0
0.0
0.0
2.0
0.0
4.0
0.0
Payoff 2.8
Choice Alternatives
Choice Alternatives
Mental Map at the end
of period t=0
Performance Landscape
3.0
3.0
1.6
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
State =3
Choice=1
Payoff 3.2
Choice Alternatives
1.6
0.0
0.0
1.6
0.0
0.0
Payoff 2.8
Choice Alternatives
0.0
2.0
0.0
0.0
2.0
0.0
0.0
Choice Alternatives
3.01
0.0
0.0
3.01
0.0
0.0
3.01
0.0
0.0
Choice Alternatives
Mental Map at the end
2.0
2.0
0.0
0.0
2.0
0.0
0.0
Choice Alternatives
1.6
0.0
0.0
0.0
0.0
0.0
1.6
0.0
0.0
3.01
0.0
0.0
3.01
0.0
0.0
Choice Alternatives
Mental Map at the end
of period t=2
State =2
Choice=3
Payoff 3.6
Choice Alternatives
Mental Map at the end
of period t=2
State =x
0.0
of period
t=200
Immediately
locked
in to alternative 1;
never
discover
better alternative 3
3.01 the
0.0
0.0
0.0
0.0
Mental Map at the end
of period t=1
Mental Map at the end
of period t=1
State =3
0.0
Mental Map at the end
of period t=2
Dislodging
through complexity:
0.0
0.0
0.0
Payoff 3.2
0.0
2.0
Contingency State
0.0
1.6
State =x
Choice=1
Mental Map at the end
of period t=200
1.6
0.0
1.8
0.0
0.0
1.8
1.6
0.0
1.8
Choice Alternatives
Mental Map at the end
of period t=200
Dislodged from choice 1
2.0
0.0
0.0
3.01
0.0
0.0
Mental Map at the end
of period t=200
Contingency State
Choice Alternatives
0.0
Payoff 3.2
0.0
Contingency State
4.0
0.0
0.0
Contingency State
2.0
0.0
1.6
Contingency State
3.0
0.0
State =3
Choice=1
Mental Map at the end
of period t=2
State
4.0
0.0
Contingency State
2.0
0.0
Contingency State
3.0
0.0
State
4.0
Contingency State
2.0
Contingency
ContingencyState
State
Contingency State
3.0
Mental Map at the end
of period t=1
Contingency State
Mental Map at the end
of period t=0
Performance Landscape
•
3.0
No-interaction landscape:
Choice Alternatives
State
•
Contingency State
Illustration of Lock-in
andLandscape
Dislodging with Correctly Specified Mental Model
Performance
1.6
0.0
4.01
0.0
0.0
4.01
1.6
0.0
4.01
Choice Alternatives
Contingency State
Performance Landscape
3.0
2.0
4.0
Dislodging caused
by4.0a Neurotic Mental Model
1.0
2.0
4.0
Choice Alternatives
Contingency State
Mental Map at the end
of period t=0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
State =3
Choice=1
Payoff 3.2
Choice Alternatives
Mental Map at the end
of period t=1
1.6
0.0
0.0
0.0
0.0
0.0
1.6
0.0
0.0
State =2
Choice=3
Payoff 3.6
Choice Alternatives
Mental Map at the end
of period t=2
1.6
0.0
1.8
0.0
0.0
1.8
1.6
0.0
1.8
Choice Alternatives
Mental Map at the end
of period t=200
Contingency State
2.0
0.0
Mental Map at the end
of period t=2
Contingency State
3.0
0.0
Mental Map at the end
of period t=1
1.6
0.0
4.01
0.0
0.0
4.01
1.6
0.0
4.01
Choice Alternatives
Mental Map at the end
of period t=200
Contingency State
4.0
Choice Alternatives
Contingency State
2.0
4.0
Contingency State
3.0
1.0
Contingency State
4.0
Contingency State
Contingency State
2.0
2.0
Mental Map at the end
of period t=0
Performance Landscape
3.0
3.0
3.01 0.0
0.0
0.0 dislodging
0.0
1.6
0.0
0.0
• 0.0The
occurs
regardless 2.0of 0.0
the0.0true performance
landscape (state
3.01 0.0
0.0
0.0
0.0
0.0
0.0
2.0
0.0
0.0
2, 0.0
choice
1 never1.6happened)
Payoff 3.2
Payoff 2.8
State =3
Choice=1
0.0
0.0
0.0
Choice Alternatives
State =x
Choice=1
1.6
0.0
0.0
Choice Alternatives
2.0
0.0
0.0
Choice Alternatives
3.01
0.0
0.0
Choice Alternatives
• For instance, it also occurs, if the performance landscape has no complexity
Contingency State
Performance Landscape
3.0
2.0
4.0
Dislodging caused
by4.0a Neurotic Mental Model
1.0
2.0
4.0
Choice Alternatives
Contingency State
Mental Map at the end
of period t=0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
State =3
Choice=1
Payoff 3.2
Choice Alternatives
Mental Map at the end
of period t=1
1.6
0.0
0.0
0.0
0.0
0.0
1.6
0.0
0.0
State =2
Choice=3
Payoff 3.6
Choice Alternatives
Mental Map at the end
of period t=2
1.6
0.0
1.8
0.0
0.0
1.8
1.6
0.0
1.8
Choice Alternatives
Mental Map at the end
of period t=200
Contingency State
2.0
0.0
Mental Map at the end
of period t=2
Contingency State
3.0
0.0
Mental Map at the end
of period t=1
1.6
0.0
4.01
0.0
0.0
4.01
1.6
0.0
4.01
Choice Alternatives
Mental Map at the end
of period t=200
Contingency State
4.0
Choice Alternatives
Contingency State
2.0
4.0
Contingency State
3.0
Contingency State
4.0
Contingency State
Contingency State
2.0
2.0
Mental Map at the end
of period t=0
Performance Landscape
3.0
3.0
3.01 0.0
0.0
0.0 dislodging
0.0
1.6
0.0
0.0
• 0.0The
occurs
regardless 2.0of 0.0
the0.0true performance
landscape (state
3.01 0.0
0.0
0.0
0.0
0.0
0.0
2.0
0.0
0.0
2, 0.0
choice
1 never1.6happened)
Payoff 3.2
Payoff 2.8
State =3
Choice=1
0.0
0.0
0.0
Choice Alternatives
State =x
Choice=1
1.6
0.0
0.0
Choice Alternatives
2.0
0.0
0.0
Choice Alternatives
3.01
0.0
0.0
Choice Alternatives
• For instance, it also occurs, if the performance landscape has no complexity
• But this implies, that an overspecified (neurotic) mental model might
outperform a correctly specified mental model!
Results for Neurotic Mental Models
1
1
systematic excess complexity
correct mental model
non-spreading overspecification
0.98
overspecified mental model
0.98
Performance in t=200
Performance in t=200
0.96
0.94
0.92
0.96
0.94
0.92
0.9
0.9
0.88
0.86
0
•
0.2
0.4
0.6
0.8
Degree of Overspecification
Overspecification is particularly
beneficial if it leads to spreading
of experiences across
contingency states (shown here
for p = 0)
1
0.88
0
0.2
0.4
0.6
Complexity
0.8
1
• The benefit of overspecified
mental models (5 different
entries) is highest in non-complex
environments
Internal Contingencies
Mental Model
Correctly Specified
No Interactions Assumed
Payoff Staffing
2.0
2.0
-2.0
1.0
3.0
-4.0
-1.0
2.0
1.0
-1.0
-2.0
-3.0
1.0
6.0
2.0
Marketing Strategy
Payoff 2.0=
-4.2 (Staffing)+
6.4 (Marketing)
Staffing Strategy
1.0
In t = 1, the manager
chooses marketing strategy
2 and staffing strategy 1
0.0
0.0
0.0
0.0
-2.1
0.0
2.0
6.0
3.0
1.0
-4.0
-2.0
4.0
2.0
1.0
Marketing Strategy
0.0
0.0
0.0
0.0
0.0
-2.1
-2.1
-2.1
Payoff Marketing
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3.2
0.0
Payoff Combined
Payoff Combined
0.0
Marketing Strategy
Marketing Strategy
Staffing Strategy
Staffing Strategy
0.0
Payoff Marketing
Payoff Marketing
Staffing Strategy
0.0
Marketing Strategy
Marketing Strategy
•
•
•
•
0.0
Staffing Strategy
4.0
Payoff Staffing
0.0
3.2
0.0
0.0
3.2
0.0
0.0
3.2
0.0
Marketing Strategy
Payoff Combined
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1.1
0.0
Marketing Strategy
Staffing Strategy
1.0
Staffing Strategy
Staffing Strategy
Payoff Staffing
Staffing Strategy
Performance Landscape
0.0
3.2
0.0
0.0
3.2
-0.0
-2.1
1.1
-2.1
Marketing Strategy
Two performance landscapes & combined
Two mental maps & combined
Manager can observe individual payoffs (and hence update individual maps)
Manager maximizes combined payoff
Long-run Results for Internal Contingencies
1.9
no-interaction mental model
correct mental model
full interaction mental model
1.8
Performance in t=200
1.7
1.6
1.5
1.4
1.3
0
•
•
•
•
0.1
0.2
0.3
0.4
0.6
0.5
Internal Complexity
0.7
0.8
0.9
1
For the no-interaction and correct mental model, performance is decreasing in
complexity
Performance is fairly insensitive to changes in complexity for the full-interaction
mental model
No-interaction model outperforms the correct and full-interaction model!
Overspecification is quite costly even in the long-run (particularly if complexity is
low)
Underspecification Creates Dislodging on Complex Landscapes
Performance Landscape
Mental Model
Correctly Specified
No Interactions Assumed
Payoff Staffing
2
2.7
-2.9
1.8
1
3.2
-4.1
-1.7
1
2
3
Marketing Alternatives
1.3
2.7
1.9
2
-1.3
-2.9
-3.2
1
1.1
6.7
2.5
1
2
3
Marketing Alternatives
Staffing Alternatives
•
In t = 1, the manager
chooses marketing strategy
2 and staffing strategy 1
Staffing Alternatives
Staffing Alternatives
3
0.0
0.0
2
0.0
0.0
0.0
1
0.0
-2.1
0.0
1
2
3
Marketing Alternatives
3
2.4
7.0
4.7
2
1.4
-5.8
-1.8
1
2.1
2.6
0.8
1
2
3
Marketing Alternatives
3
0.0
0.0
0.0
2
0.0
0.0
0.0
1
-2.1
-2.1
-2.1
1
2
3
Marketing Alternatives
Payoff Marketing
3
0.0
0.0
0.0
2
0.0
0.0
0.0
1
0.0
3.2
0.0
1
2
3
Marketing Alternatives
Payoff Combined
Payoff Combined
•
0.0
Payoff Marketing
Payoff Marketing
•
3
Staffing Alternatives
2.8
Staffing Alternatives
4.3
Payoff Staffing
3
0.0
3.2
0.0
2
0.0
3.2
0.0
1
0.0
3.2
0.0
1
2
3
Marketing Alternatives
Payoff Combined
3
0.0
0.0
0.0
2
0.0
0.0
0.0
1
0.0
1.1
0.0
1
2
3
Marketing Alternatives
Staffing Alternatives
1.1
Staffing Alternatives
3
Staffing Alternatives
Staffing Alternatives
Payoff Staffing
3
0.0
3.2
0.0
2
0.0
3.2
-0.0
1
-2.1
1.1
-2.1
1
2
3
Marketing Alternatives
Underspecification can yield increased exploration if one activity provides a positive return, the
other a negative return, and the sum of both is positive
With an underspecified mental model, the manager wrongly assumes that the high
performance of the first activity could also be achieved if the other activity is differently
configured
With a correctly specified mental model, the manager would stick to this combination of
activities
Robustness
•
•
•
•
•
•
•
•
Performance = % times best choice (given contingency) found
Number of choices and contingencies
Variance of performance means in landscape
Variance of performance signals
Initial beliefs (randomly drawn from N(0, 1) rather than 0)
Different updating mechanism (weight recent experience more)
Different choice mechanism (softmax rule)
Different ways of breaking ties (choose alternative played
most/least often; choose alternative that would update most/least
entries in mental map)
25
Result Summary
•
A correct mental model of contingencies does not always lead to
highest performance
•
External contingencies
– In the presence of few interdependencies, being slightly neurotic (i.e., having
a slightly overspecified mental model) can increase performance
•
Internal contingencies
– In the presence of many interdependencies, having blind spots (i.e., having
an underspecified mental model) can increase performance
Conclusion
•
•
•
•
•
Intriguing result:
NK/complementarity work tends to paint a very pessimistic picture
of managers getting quickly stuck on low, local peaks in landscapes
that have many interdependencies
In prior work, I have looked at how different organizational designs
can help firms avoid getting stuck too quickly
Here, we show that underspecified mental models can create
helpful exploration and thus help firms avoid getting stuck to quickly
Thus, firms might not perform as poorly as we might have expected
otherwise
Back-up slides
Prior Multi-armed Bandit Models
•
•
Classical set up: Decision maker faces N alternatives (“arms”),
each with unknown, independent payoffs. How should the decision
maker best allocate choices over time?
Extensions:
–
–
–
–
–
•
•
Arm-acquiring bandits (over time, more alternatives appear)
Branching arms (chosen alternatives may create new alternatives)
Restless bandits (payoffs of unplayed alternatives may change)
Switching costs
Correlated arms (information on one arm can be used for another)
All are concerned with finding the optimal choice policy
We use “greedy” choice policy and are concerned with beliefs over
correlation
– Meyer and Shi (1995) find undersampling
•
•
P = 0 and correct mental model  5-armed, standard bandit model
P = 1 and correct mental model  five independent 5-armed
standard bandit models
Short-run looks similar
1.9
no-interaction mental model
correct mental model
full interaction mental model
1.8
Performance in t=20
1.7
1.6
1.5
1.4
1.3
0
0.1
0.2
0.3
0.4
0.5
0.6
Internal Complexity
0.7
0.8
0.9
1
How to Overspecify a Mental Model
Need to create dislodging => don’t have quickly an opinion on everything
Need to create spreading => new experiences need to apply elsewhere
2.0
4.0
3.0
2.0
4.0
Systematic
Mental
Map at the end
ofoverspecification
period t=1
Contingency State
Mental Map at the end
of period t=0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Choice Alternatives
0.0
0.0
0.0
Payoff 3.2
0.0
Choice Alternatives
State =3
Choice=1
Payoff 3.2
1.6
0.0
0.0
1.6
0.0
0.0
1.6
0.0
0.0
Choice Alternatives
State =x
Choice=1
Payoff 2.8
0.0
0.0
0.0
1.6
0.0
0.0
1.6
0.0
0.0
0.0 0.00.0 0.0
2.0
Mental Map at the end
of period t=1
Payoff 3.2
0.0
0.0
Choice2.0
Alternatives
2.0
0.0
Payoff 4.2
Choice Alternatives
State =1
0.0
0.0
0.0
0.0
0.0
0.0
Mental Map at the end Choice=1 Mental Map at the end
of period t=200
of0.0
period0.0
t=2 0.0
1.6
0.0
0.0
0.0
State =3
Choice=3
0.0
Choice Alternatives
3.01 1.6
0.0
0.0
0.0
0.0
3.01Choice
0.0 Alternatives
0.0
3.01
0.0
0.0
Choice Alternatives
Contingency State
0.0
Mental Map at the end
of period t=0
Choice Alternatives
0.0
0.0
State =1
Choice=1
Mental Map at the end
of period t=2
0.0
0.0
2.1
1.6
0.0
0.0
1.6
0.0
0.0
Choice Alternatives
Mental Map at the end
of period t=2
State =3
Choice=3
Payoff 4.2
Contingency State
3.0
0.0
Contingency State
4.0
0.0
Contingency State
2.0
Contingency State
3.0
Contingency State
Contingency State
Performance Landscape
0.0
Mental Map at the end
of period t=1
Contingency State
Non-spreading
overspecfication
Contingency State
Mental Map at the end
of period t=0
Contingency State
•
•
0.0
0.0
2.1
1.6
0.0
2.1
1.6
0.0
0.0
Choice Alternatives
How to Overspecify a Mental Model
Need to create dislodging => don’t have quickly an opinion on everything
Need to create spreading => new experiences need to apply elsewhere
2.0
4.0
3.0
2.0
4.0
Systematic
Mental
Map at the end
ofoverspecification
period t=1
Contingency State
Mental Map at the end
of period t=0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Choice Alternatives
0.0
0.0
0.0
Payoff 3.2
0.0
Choice Alternatives
State =3
Choice=1
Payoff 3.2
1.6
0.0
0.0
1.6
0.0
0.0
1.6
0.0
0.0
Choice Alternatives
State =x
Choice=1
Payoff 2.8
0.0
0.0
0.0
1.6
0.0
0.0
1.6
0.0
0.0
0.0 0.00.0 0.0
2.0
Mental Map at the end
of period t=1
Payoff 3.2
0.0
0.0
Choice2.0
Alternatives
2.0
0.0
Payoff 4.2
Choice Alternatives
State =1
0.0
0.0
0.0
0.0
0.0
0.0
Mental Map at the end Choice=1 Mental Map at the end
of period t=200
of0.0
period0.0
t=2 0.0
1.6
0.0
0.0
0.0
State =3
Choice=3
0.0
Choice Alternatives
3.01 1.6
0.0
0.0
0.0
0.0
3.01Choice
0.0 Alternatives
0.0
3.01
0.0
0.0
Choice Alternatives
Contingency State
0.0
Mental Map at the end
of period t=0
Choice Alternatives
0.0
0.0
State =1
Choice=1
Mental Map at the end
of period t=2
0.0
0.0
2.1
1.6
0.0
0.0
1.6
0.0
0.0
Choice Alternatives
Mental Map at the end
of period t=2
State =3
Choice=3
Payoff 4.2
Contingency State
3.0
0.0
Contingency State
4.0
0.0
Contingency State
2.0
Contingency State
3.0
Contingency State
Contingency State
Performance Landscape
0.0
Mental Map at the end
of period t=1
Contingency State
Non-spreading
overspecfication
Contingency State
Mental Map at the end
of period t=0
Contingency State
•
•
0.0
0.0
2.1
1.6
0.0
2.1
1.6
0.0
0.0
Choice Alternatives
Costs of Misspecification
•
Over- and underspecified mental models lead to costs but they also
can create benefits
Costs:
• Underspecified mental models (“incorrect pooling of experience”;
“incorrect inferences”):
– Managers choose actions that are good on average, even though for each
state there may exist an even better solution
– Inappropriately apply experiences of one state to another
•
Overspecified mental models (“everything is a special case”):
– Tends to slow down the improvement of decision making
– Makes estimates noisy (smaller N per cell)
– Does not exploit existing correlation between outcomes
– Suppresses exploration (in the case of internal contingencies)
Benefits of Misspecification and their Mechanisms
•
Benefits: Misspecified mental models can lead to increased
exploration
•
External contingencies
– Overspecification prevents quick lock-in (by prolonging ignorance/ “an open
mind” in the mental map; yet need to also spread the new experience)
•
Internal contingencies
– Underspecification prevents quick lock-in (by pulling managers away from
combinations that performed well and luring them to other, supposedly even
better combinations)
•
Different mechanisms are due to the sampling process
– External contingencies: forced experiences with not-yet-tried choices (so
overspecification can create dislodging)
– Internal contingencies: full control over the sampling process (as a result,
overspecification only leads to less spreading of experience, which in turn
reduces likelihood of dislodging)
Exploration with Internal Contingencies
0.19
6
% of all combinations
tried
by t =by
200
number
of combinations
played
t = 200
0.18
5.5
no-interaction mental model
correct mental model
full interaction mental model
0.17
5
0.16
4.5
4
0.15
3.5
0.14
3
0.13
2.5
0.12
2
0.11
1.5
0.1
1 0
0
0.1
0.1
0.2
0.2
0.3
0.3
0.4
0.5
0.6
0.4 Internal
0.5Complexity
0.6
0.7
0.7
0.8
0.8
0.9
0.9
1
1