Why scientists chase big problems (and why it matters)

Carl Bergstrom
Carl BergstromProfessor of Biology at University of Washington
Why scientists
chase big
problems
(and why it matters)
Modeling Science,Technology, and Innovation
National Academy of Sciences
May 17-18, 2016 CarlT. Bergstrom
Washington, DC University of Washington
Jacob Foster
Department of Sociology
UCLA
Yangbo Song
School of Management & Economics
Hong Kong University of China
What
motivates
scientists?
Imagination Reality
These days, scientists do research to
get grants, rather than vice versa.
Given that scientists are epistemically sullied, how
do the incentives created by contemporary
scientific institutions lead scientists to allocate
research effort across problems?
“
Are scientist, like Adam Smith’s
economic actors,
led by an invisible hand to
promote an end which was
no part of [their] intention” ?
A theoretical framework for
Science of Science Policy
Hot problems: examples
•  How does DNA encode amino acid sequence?
•  What is the etiological agent of AIDS?
•  How do we explain the Lamb shift?
•  Does Zika virus cause microcephaly and if so, how?
Hot problems: properties
•  Well-defined in scope
•  Widely agreed to be important within the
scientific community
•  More rewarding than day-to-day work.
•  Not a “grind” – unclear how to solve.
•  May be immediately useful to society at large,
but need not be.
•  Pull scientists away from other ongoing
research
Model setup: the credit race game
…n scientists
One focal problem
Continuous time
outside
options
All start at
the same time
First to solve
gets all the credit.
Others get zero.
Model setup
…n scientists
outside
options
Scientists aim to maximize the credit they receive.
Scientists vary in the amount of scientific capital hi
they can bring to bear upon a problem.
h1 h2 h3 hn-1 hn
Outside option pays off in credit at rate hi x
Model setup
Scientists who pursue focal problem pay a startup cost F.
Constant instantaneous probability of solution hi /d
where d is the difficulty of the problem.
The expected
time to solution τ
by someone is then
τ
Solver gets payoff V. Everyone else gets 0.
Probability that scientist j wins the race is hj /Σ hi .
Model setup
Where I’ is the set of scientists who pursue the problem,
expected payoff Ui to scientist i of pursuing the problem is
Reward Chance
of winning
Cost of entryExpected
duration
Opportunity
cost
Model setup
A Nash equilibrium of the credit race game is a subset I* of
scientists such that those in I* and no others do better to
pursue the focal problem rather than their outside options.
Every participant does better to stay in
Every non-participant does better to stay out
Proposition 1. A Nash equilibrium always
exists in the credit race game.
Example 1
Mysterious symbols are
found in Paleolithic cave
art. They seem to be
some kind of code.
Paleolinguists Alice (F.R.S),
Bob (assistant professor),
and Carol (Miller fellow)
could drop everything and
try to decode them.
Image:Alexander Putney, Sanskrit
Paleolithic code example
Alice has capital 10
Bob has capital 5 Value V=20 Difficulty d=5
Carol has capital 4 Fixed cost F=4 Opportunity cost x=1
Nash equilibria, and associated payoffs, are as follows:
U(Alice) U(Bob) U(Carol)
{Alice, Bob} 6 1 (-0.84)
{Alice, Carol} 6.71 (-0.05) 0.29
but not
{Bob, Carol} (3.89) 4.33 2.67
With multiple equilibria, how can we derive
predictive value from our model?
We need some method for equilibrium selection.
Risk dominance
The risk dominant Nash equilibrium is the one
with the largest basin of attraction.
It is the one for which the cost of making the
wrong move – or wrongly behaving as if you
were at a different equilibrium – is the largest.
Proposition 2. A unique risk dominant
equilibrium exists in the game.
At this equilibrium, the individuals with
the highest scientific capital pursue the
problem and all others opt out.
Paleolithic code example
High costs
of switching
Low costs
of switching
Unique risk dominant equilibrium is {Alice, Bob}
U(Alice) U(Bob) U(Carol)
{Alice, Bob} 6 1 (-0.84)
{Alice, Carol} 6.71 (-0.05) 0.29
Top researchers chase hot topics
Extension
…scientists
outside
options
Scientists vary not only in their scientific capital, but
also in the productivity of their normal work.
That is, the value of outside options is an increasing
function of scientific capital xi=χ(hi) with χ’(hi)>0.
h1 h2 h3 hn-1 hn
x1 x2 x3 xn-1 xn
Proposition 3. When outside options
differ, the equilibrium I* composed of
scientists with highest capital is the unique
risk dominant equilibrium provided that
hiχ(hi) is concave and
Publishing partial results
The huge difference between academic credit
races and patent races is that in academia
we are credited for being cited, not for some
final product.Thus it can often be in our interest
to publish partial results.
Publishing partial results
The focal problem now comes in stages that
must be solved sequentially. Scientists
have the option of publishing after
completing any stage, or they may
wait until solving the entire problem. If
they publish intermediate results, they are
guaranteed credit for that result but others
can then move immediately to the next stage.
4.3.2.1.
Stage1 Stage 2 Stage 3
Publishing partial results
A public sharing equilibrium (PSE) is an
equilibrium in which all participants publish
immediately upon solving any stage.
For stage m of a problem, let I*
m be the set
{1,2,…i*
m} of participants in that stage:
Publishing partial results
For stage m of a problem, let I*
m be the set
{1,2,…i*
m} of participants in that stage:
Proposition 4. The unique risk dominant
equilibrium is the PSE in which scientists in I*
m
participate in stage m, provided that for each
consecutive pair of stages m and m’,
Publishing partial results
A researcher will publish partial results when
•  When a stage is relatively valuable (Vm>Vm’)
or easy (dm<dm’).
•  When there are many competitors and/or
competitors with high scientific capital
•  When she has low scientific capital
•  When the opportunity cost is low
Example 2
An unknown disease strikes a dozen
people in Louisiana, many of them
golfers. It causes temporary paralysis
and long-term joint pain. To take
preventative action, we must solve a
two-stage problem:
1)  What is causing this disease?
2)  And where is it coming from?
Two teams, one from CDC, and one
from LSU are well-poised to solve
this mystery.
Image:Alexander Putney, Sanskrit
Louisiana golfer example
CDC has capital 12 Values V1=V2=30 Difficulty D1=D2=15
LSU has capital 5 Fixed costs F1=4, F2=8 Opp. costs x=1
Only public sharing equilibrium in this game:
Both CDC and LSU attempt stage 1. Whichever solves
it first publishes immediately. Regardless of who solved
stage 1, only CDC attempts stage 2 (and obviously
publishes immediately.)
Louisiana golfer example
CDC has capital 12 Values V1=V2=30 Difficulty D1=D2=15
LSU has capital 5 Startup costs F1=4, F2=8 Opp. costs x=1
If researchers were not allowed to publish partial results:
The only equilibrium has the CDC attempting the
problem and LSU opting out. Here we see a partial
publication norm recruiting increased effort to the
problem.
Social welfare
(the “why it matters” part)
In our model (as in life, largely) scientists are
looking out for their own interests. How does
this align with society’s interests?
Because we model scientists’ outside options,
we are in a position to consider this question
explicitly.
Social welfare
Research creates knowledge, generating a (discounted)
flow of value indefinitely onward into the future.
Where K(t) is knowledge
at time t, social welfare W is
Social welfare
Working on a hot problem interrupts daily progress, in
exchange for a larger subsequent jump in knowledge
when the hot problem is solved.
Social welfare
Where is the social value, is the social
opportunity cost, and is the social cost of
startup, the social welfare when scientists {1,2,
…i} with total capital Hi work on the hot
problem is
Discounted Reward Cost of entry
for i scientists
Discounted
opportunity cost
Proposition 5. There is a unique social
optimum, in which the ie scientists with
the highest scientific capital work on the
hot problem and the rest opt out.
Social welfare results
How does the risk dominant equilibrium (what
scientists will do) compare with the socially
optimum (what we would like them to do)?
Both under-participation and over-participation
are possible. Roughly (ignoring some subtle
discounting terms) we see under-participation
when
Example 3
Halibut fisheries in Alaska abruptly
collapse. This poses a two-stage
problem:
1)  What is causing the collapse?
Climate change? Disease?
Overfishing?
2)  What can we do about it?
Teams from NMFS and UW are
able to attack the problem.
Image:Alexander Putney, SanskritImage (cc) flickr: Steve Johnson
Halibut fishery example
NMFS has capital 10 Values V1=60 V2=30 Diff. D1=D2=15
UW has capital 6 Startup costs F1=1, F2=6 Opp. costs x=1
Value to society =100.
Only public sharing equilibrium in this game:
NMFS and UW attempt stage 1. Whichever solves it
first publishes immediately. Regardless of who solved
stage 1, only NMFS attempts stage 2 (and obviously
publishes immediately.) Social welfare is W=122.94
Halibut fishery example
NMFS has capital 10 Values V1=60 V2=30 Diff. D1=D2=15
UW has capital 6 Startup costs F1=1, F2=6 Opp. costs x=1
Value to society =100.
If we don’t allow partial progress sharing, both teams
attempt the entire problem. In this case, the expected
time to solution is shorter, and social welfare is higher
W=126.98!
Contrary to conventional wisdom,
Proposition 6. Allowing partial progress
sharing does not necessarily accelerate
the rate at which a hot problem is solved.
Why not?
Monument to the
conquerors of
space (1964)
Image:russianuniverse.org
Future directions
Problems of unknown difficulty
–  Why scientists give up on a problem
–  Strategic informational issues around non-
publication.
Reproducibility
–  How do our institutions shape individual
incentives in ways that contribute to or
ameliorate the “reproducibility crisis.”
Principal-agent framework
–  How do alternative forms of credit allocation
influence scientists’ behavior?
–  What can a govt. agency do to shift scientists’
efforts toward the socially optimal allocation?
–  How does the publishing system contribute to
irreproducibility and inefficiency?
–  How do within-university institutions accelerate or
retard the progress of science?
Policy implications and suggestions
1 of 45

Recommended

Adhearsion and Telegraph Framework Presentation by
Adhearsion and Telegraph Framework PresentationAdhearsion and Telegraph Framework Presentation
Adhearsion and Telegraph Framework PresentationJustin Grammens
1.6K views33 slides
MPHE by
MPHEMPHE
MPHEMUHAMMED AHMED
563 views1 slide
Caso clinico politraumatizado ii by
Caso clinico politraumatizado iiCaso clinico politraumatizado ii
Caso clinico politraumatizado iiLenar Chavez Cieza
671 views7 slides
Bc consultation firm ppt by
Bc consultation firm pptBc consultation firm ppt
Bc consultation firm pptAimee Literato
528 views20 slides
clarity by
clarityclarity
clarityBryant Riggs
449 views4 slides
Futbol by
FutbolFutbol
FutbolDiego Fernando Lasso
232 views2 slides

More Related Content

Similar to Why scientists chase big problems (and why it matters)

Models of science by
Models of scienceModels of science
Models of scienceCarl Bergstrom
492 views77 slides
Wicked issues taming problems and systems by
Wicked issues  taming problems and systemsWicked issues  taming problems and systems
Wicked issues taming problems and systemsTim Curtis
2.9K views18 slides
China 2016: My understanding of the history of quantitative science communic... by
China 2016: My understanding of the  history of quantitative science communic...China 2016: My understanding of the  history of quantitative science communic...
China 2016: My understanding of the history of quantitative science communic...John C. Besley
159 views36 slides
Empirical Evidence of a Conditional Endowment Effect by
Empirical Evidence of a Conditional Endowment EffectEmpirical Evidence of a Conditional Endowment Effect
Empirical Evidence of a Conditional Endowment EffectStuart Landesberg
341 views54 slides
352735322 rsh-qam11-tif-03-doc by
352735322 rsh-qam11-tif-03-doc352735322 rsh-qam11-tif-03-doc
352735322 rsh-qam11-tif-03-docBookStoreLib
129 views34 slides
352735322 rsh-qam11-tif-03-doc by
352735322 rsh-qam11-tif-03-doc352735322 rsh-qam11-tif-03-doc
352735322 rsh-qam11-tif-03-docFiras Husseini
1K views34 slides

Similar to Why scientists chase big problems (and why it matters)(20)

Wicked issues taming problems and systems by Tim Curtis
Wicked issues  taming problems and systemsWicked issues  taming problems and systems
Wicked issues taming problems and systems
Tim Curtis2.9K views
China 2016: My understanding of the history of quantitative science communic... by John C. Besley
China 2016: My understanding of the  history of quantitative science communic...China 2016: My understanding of the  history of quantitative science communic...
China 2016: My understanding of the history of quantitative science communic...
John C. Besley159 views
Empirical Evidence of a Conditional Endowment Effect by Stuart Landesberg
Empirical Evidence of a Conditional Endowment EffectEmpirical Evidence of a Conditional Endowment Effect
Empirical Evidence of a Conditional Endowment Effect
Stuart Landesberg341 views
352735322 rsh-qam11-tif-03-doc by BookStoreLib
352735322 rsh-qam11-tif-03-doc352735322 rsh-qam11-tif-03-doc
352735322 rsh-qam11-tif-03-doc
BookStoreLib129 views
The Holocaust Is Remembered As One Of The Most Vicious Events by Leslie Daniels
The Holocaust Is Remembered As One Of The Most Vicious EventsThe Holocaust Is Remembered As One Of The Most Vicious Events
The Holocaust Is Remembered As One Of The Most Vicious Events
Leslie Daniels2 views
Natural sciences 2017 18 by Kieran Ryan
Natural sciences 2017 18Natural sciences 2017 18
Natural sciences 2017 18
Kieran Ryan2.2K views
Applying An Analytical Model Of A Plane Wall by Carla Bennington
Applying An Analytical Model Of A Plane WallApplying An Analytical Model Of A Plane Wall
Applying An Analytical Model Of A Plane Wall
Ansatz 2021 finals by Amrit Kumar
Ansatz 2021 finalsAnsatz 2021 finals
Ansatz 2021 finals
Amrit Kumar243 views
Essential human sciences in 2 lessons (with extension if required) by Kieran Ryan
Essential human sciences in 2 lessons (with extension if required)Essential human sciences in 2 lessons (with extension if required)
Essential human sciences in 2 lessons (with extension if required)
Kieran Ryan527 views
Essential human sciences in 2 lessons (with extension if required) by Kieran Ryan
Essential human sciences in 2 lessons (with extension if required)Essential human sciences in 2 lessons (with extension if required)
Essential human sciences in 2 lessons (with extension if required)
Kieran Ryan883 views
Quantum Models of Cognition and Decision by Catarina Moreira
Quantum Models of Cognition and DecisionQuantum Models of Cognition and Decision
Quantum Models of Cognition and Decision
Catarina Moreira787 views
Scientific Triage: How to make strategic choices about prioritizing basic sci... by nfefferman
Scientific Triage: How to make strategic choices about prioritizing basic sci...Scientific Triage: How to make strategic choices about prioritizing basic sci...
Scientific Triage: How to make strategic choices about prioritizing basic sci...
nfefferman175 views
The Theory Of Evolution Of A Population Over A Number Of... by Stefanie Yang
The Theory Of Evolution Of A Population Over A Number Of...The Theory Of Evolution Of A Population Over A Number Of...
The Theory Of Evolution Of A Population Over A Number Of...
Stefanie Yang3 views

More from Carl Bergstrom

Transforming Science Education in An Age of Misinformation by
Transforming Science Education in An Age of MisinformationTransforming Science Education in An Age of Misinformation
Transforming Science Education in An Age of MisinformationCarl Bergstrom
217 views100 slides
Peer Review Filters.pptx by
Peer Review Filters.pptxPeer Review Filters.pptx
Peer Review Filters.pptxCarl Bergstrom
853 views60 slides
Proactive COVID-19 testing to mitigate spread by
Proactive COVID-19 testing to mitigate spreadProactive COVID-19 testing to mitigate spread
Proactive COVID-19 testing to mitigate spreadCarl Bergstrom
1.1K views45 slides
Burning Money: Competition Generates Massive Inefficiencies in the Grant Pr... by
Burning Money: Competition Generates Massive Inefficiencies in the Grant Pr...Burning Money: Competition Generates Massive Inefficiencies in the Grant Pr...
Burning Money: Competition Generates Massive Inefficiencies in the Grant Pr...Carl Bergstrom
568 views44 slides
Information Technology and the Ubiquity of Bullshit by
Information Technology and the Ubiquity of BullshitInformation Technology and the Ubiquity of Bullshit
Information Technology and the Ubiquity of BullshitCarl Bergstrom
299 views54 slides
Information Concealing Games by
Information Concealing GamesInformation Concealing Games
Information Concealing GamesCarl Bergstrom
653 views64 slides

More from Carl Bergstrom(10)

Transforming Science Education in An Age of Misinformation by Carl Bergstrom
Transforming Science Education in An Age of MisinformationTransforming Science Education in An Age of Misinformation
Transforming Science Education in An Age of Misinformation
Carl Bergstrom217 views
Proactive COVID-19 testing to mitigate spread by Carl Bergstrom
Proactive COVID-19 testing to mitigate spreadProactive COVID-19 testing to mitigate spread
Proactive COVID-19 testing to mitigate spread
Carl Bergstrom1.1K views
Burning Money: Competition Generates Massive Inefficiencies in the Grant Pr... by Carl Bergstrom
Burning Money: Competition Generates Massive Inefficiencies in the Grant Pr...Burning Money: Competition Generates Massive Inefficiencies in the Grant Pr...
Burning Money: Competition Generates Massive Inefficiencies in the Grant Pr...
Carl Bergstrom568 views
Information Technology and the Ubiquity of Bullshit by Carl Bergstrom
Information Technology and the Ubiquity of BullshitInformation Technology and the Ubiquity of Bullshit
Information Technology and the Ubiquity of Bullshit
Carl Bergstrom299 views
Information Concealing Games by Carl Bergstrom
Information Concealing GamesInformation Concealing Games
Information Concealing Games
Carl Bergstrom653 views
Citation metrics and the stories they tell by Carl Bergstrom
Citation metrics and the stories they tellCitation metrics and the stories they tell
Citation metrics and the stories they tell
Carl Bergstrom3.7K views
It's all a game: The twin fallacies of epistemic purity and the scholarly inv... by Carl Bergstrom
It's all a game: The twin fallacies of epistemic purity and the scholarly inv...It's all a game: The twin fallacies of epistemic purity and the scholarly inv...
It's all a game: The twin fallacies of epistemic purity and the scholarly inv...
Carl Bergstrom725 views
Anthropogenic evolution, externalities, and public health by Carl Bergstrom
Anthropogenic evolution, externalities, and public healthAnthropogenic evolution, externalities, and public health
Anthropogenic evolution, externalities, and public health
Carl Bergstrom547 views
Navigating science using citation networks by Carl Bergstrom
Navigating science using citation networksNavigating science using citation networks
Navigating science using citation networks
Carl Bergstrom3.1K views

Recently uploaded

Evaluation and Standardization of the Marketed Polyherbal drug Patanjali Divy... by
Evaluation and Standardization of the Marketed Polyherbal drug Patanjali Divy...Evaluation and Standardization of the Marketed Polyherbal drug Patanjali Divy...
Evaluation and Standardization of the Marketed Polyherbal drug Patanjali Divy...Anmol Vishnu Gupta
8 views10 slides
Oral_Presentation_by_Fatma (2).pdf by
Oral_Presentation_by_Fatma (2).pdfOral_Presentation_by_Fatma (2).pdf
Oral_Presentation_by_Fatma (2).pdffatmaalmrzqi
8 views7 slides
Presentation on experimental laboratory animal- Hamster by
Presentation on experimental laboratory animal- HamsterPresentation on experimental laboratory animal- Hamster
Presentation on experimental laboratory animal- HamsterKanika13641
6 views8 slides
Study on Drug Drug Interaction Through Prescription Analysis of Type II Diabe... by
Study on Drug Drug Interaction Through Prescription Analysis of Type II Diabe...Study on Drug Drug Interaction Through Prescription Analysis of Type II Diabe...
Study on Drug Drug Interaction Through Prescription Analysis of Type II Diabe...Anmol Vishnu Gupta
28 views12 slides
NUTRITION IN BACTERIA.pdf by
NUTRITION IN BACTERIA.pdfNUTRITION IN BACTERIA.pdf
NUTRITION IN BACTERIA.pdfNandadulalSannigrahi
39 views14 slides

Recently uploaded(20)

Evaluation and Standardization of the Marketed Polyherbal drug Patanjali Divy... by Anmol Vishnu Gupta
Evaluation and Standardization of the Marketed Polyherbal drug Patanjali Divy...Evaluation and Standardization of the Marketed Polyherbal drug Patanjali Divy...
Evaluation and Standardization of the Marketed Polyherbal drug Patanjali Divy...
Oral_Presentation_by_Fatma (2).pdf by fatmaalmrzqi
Oral_Presentation_by_Fatma (2).pdfOral_Presentation_by_Fatma (2).pdf
Oral_Presentation_by_Fatma (2).pdf
fatmaalmrzqi8 views
Presentation on experimental laboratory animal- Hamster by Kanika13641
Presentation on experimental laboratory animal- HamsterPresentation on experimental laboratory animal- Hamster
Presentation on experimental laboratory animal- Hamster
Kanika136416 views
Study on Drug Drug Interaction Through Prescription Analysis of Type II Diabe... by Anmol Vishnu Gupta
Study on Drug Drug Interaction Through Prescription Analysis of Type II Diabe...Study on Drug Drug Interaction Through Prescription Analysis of Type II Diabe...
Study on Drug Drug Interaction Through Prescription Analysis of Type II Diabe...
ELECTRON TRANSPORT CHAIN by DEEKSHA RANI
ELECTRON TRANSPORT CHAINELECTRON TRANSPORT CHAIN
ELECTRON TRANSPORT CHAIN
DEEKSHA RANI16 views
Applications of Large Language Models in Materials Discovery and Design by Anubhav Jain
Applications of Large Language Models in Materials Discovery and DesignApplications of Large Language Models in Materials Discovery and Design
Applications of Large Language Models in Materials Discovery and Design
Anubhav Jain14 views
2. Natural Sciences and Technology Author Siyavula.pdf by ssuser821efa
2. Natural Sciences and Technology Author Siyavula.pdf2. Natural Sciences and Technology Author Siyavula.pdf
2. Natural Sciences and Technology Author Siyavula.pdf
ssuser821efa12 views
Determination of color fastness to rubbing(wet and dry condition) by crockmeter. by ShadmanSakib63
Determination of color fastness to rubbing(wet and dry condition) by crockmeter.Determination of color fastness to rubbing(wet and dry condition) by crockmeter.
Determination of color fastness to rubbing(wet and dry condition) by crockmeter.
ShadmanSakib636 views
Indian council for child welfare by RenuWaghmare2
Indian council for child welfareIndian council for child welfare
Indian council for child welfare
RenuWaghmare27 views
Small ruminant keepers’ knowledge, attitudes and practices towards peste des ... by ILRI
Small ruminant keepers’ knowledge, attitudes and practices towards peste des ...Small ruminant keepers’ knowledge, attitudes and practices towards peste des ...
Small ruminant keepers’ knowledge, attitudes and practices towards peste des ...
ILRI9 views
Best Hybrid Event Platform.pptx by Harriet Davis
Best Hybrid Event Platform.pptxBest Hybrid Event Platform.pptx
Best Hybrid Event Platform.pptx
Harriet Davis10 views
Ellagic Acid and Its Metabolites as Potent and Selective Allosteric Inhibitor... by Trustlife
Ellagic Acid and Its Metabolites as Potent and Selective Allosteric Inhibitor...Ellagic Acid and Its Metabolites as Potent and Selective Allosteric Inhibitor...
Ellagic Acid and Its Metabolites as Potent and Selective Allosteric Inhibitor...
Trustlife154 views

Why scientists chase big problems (and why it matters)

  • 1. Why scientists chase big problems (and why it matters) Modeling Science,Technology, and Innovation National Academy of Sciences May 17-18, 2016 CarlT. Bergstrom Washington, DC University of Washington
  • 2. Jacob Foster Department of Sociology UCLA Yangbo Song School of Management & Economics Hong Kong University of China
  • 4. These days, scientists do research to get grants, rather than vice versa.
  • 5. Given that scientists are epistemically sullied, how do the incentives created by contemporary scientific institutions lead scientists to allocate research effort across problems?
  • 6. “ Are scientist, like Adam Smith’s economic actors, led by an invisible hand to promote an end which was no part of [their] intention” ?
  • 7. A theoretical framework for Science of Science Policy
  • 8. Hot problems: examples •  How does DNA encode amino acid sequence? •  What is the etiological agent of AIDS? •  How do we explain the Lamb shift? •  Does Zika virus cause microcephaly and if so, how?
  • 9. Hot problems: properties •  Well-defined in scope •  Widely agreed to be important within the scientific community •  More rewarding than day-to-day work. •  Not a “grind” – unclear how to solve. •  May be immediately useful to society at large, but need not be. •  Pull scientists away from other ongoing research
  • 10. Model setup: the credit race game …n scientists One focal problem Continuous time outside options All start at the same time First to solve gets all the credit. Others get zero.
  • 11. Model setup …n scientists outside options Scientists aim to maximize the credit they receive. Scientists vary in the amount of scientific capital hi they can bring to bear upon a problem. h1 h2 h3 hn-1 hn Outside option pays off in credit at rate hi x
  • 12. Model setup Scientists who pursue focal problem pay a startup cost F. Constant instantaneous probability of solution hi /d where d is the difficulty of the problem. The expected time to solution τ by someone is then τ Solver gets payoff V. Everyone else gets 0. Probability that scientist j wins the race is hj /Σ hi .
  • 13. Model setup Where I’ is the set of scientists who pursue the problem, expected payoff Ui to scientist i of pursuing the problem is Reward Chance of winning Cost of entryExpected duration Opportunity cost
  • 14. Model setup A Nash equilibrium of the credit race game is a subset I* of scientists such that those in I* and no others do better to pursue the focal problem rather than their outside options. Every participant does better to stay in Every non-participant does better to stay out
  • 15. Proposition 1. A Nash equilibrium always exists in the credit race game.
  • 16. Example 1 Mysterious symbols are found in Paleolithic cave art. They seem to be some kind of code. Paleolinguists Alice (F.R.S), Bob (assistant professor), and Carol (Miller fellow) could drop everything and try to decode them. Image:Alexander Putney, Sanskrit
  • 17. Paleolithic code example Alice has capital 10 Bob has capital 5 Value V=20 Difficulty d=5 Carol has capital 4 Fixed cost F=4 Opportunity cost x=1 Nash equilibria, and associated payoffs, are as follows: U(Alice) U(Bob) U(Carol) {Alice, Bob} 6 1 (-0.84) {Alice, Carol} 6.71 (-0.05) 0.29 but not {Bob, Carol} (3.89) 4.33 2.67
  • 18. With multiple equilibria, how can we derive predictive value from our model? We need some method for equilibrium selection.
  • 19. Risk dominance The risk dominant Nash equilibrium is the one with the largest basin of attraction. It is the one for which the cost of making the wrong move – or wrongly behaving as if you were at a different equilibrium – is the largest.
  • 20. Proposition 2. A unique risk dominant equilibrium exists in the game. At this equilibrium, the individuals with the highest scientific capital pursue the problem and all others opt out.
  • 21. Paleolithic code example High costs of switching Low costs of switching Unique risk dominant equilibrium is {Alice, Bob} U(Alice) U(Bob) U(Carol) {Alice, Bob} 6 1 (-0.84) {Alice, Carol} 6.71 (-0.05) 0.29
  • 22. Top researchers chase hot topics
  • 23. Extension …scientists outside options Scientists vary not only in their scientific capital, but also in the productivity of their normal work. That is, the value of outside options is an increasing function of scientific capital xi=χ(hi) with χ’(hi)>0. h1 h2 h3 hn-1 hn x1 x2 x3 xn-1 xn
  • 24. Proposition 3. When outside options differ, the equilibrium I* composed of scientists with highest capital is the unique risk dominant equilibrium provided that hiχ(hi) is concave and
  • 25. Publishing partial results The huge difference between academic credit races and patent races is that in academia we are credited for being cited, not for some final product.Thus it can often be in our interest to publish partial results.
  • 26. Publishing partial results The focal problem now comes in stages that must be solved sequentially. Scientists have the option of publishing after completing any stage, or they may wait until solving the entire problem. If they publish intermediate results, they are guaranteed credit for that result but others can then move immediately to the next stage. 4.3.2.1. Stage1 Stage 2 Stage 3
  • 27. Publishing partial results A public sharing equilibrium (PSE) is an equilibrium in which all participants publish immediately upon solving any stage. For stage m of a problem, let I* m be the set {1,2,…i* m} of participants in that stage:
  • 28. Publishing partial results For stage m of a problem, let I* m be the set {1,2,…i* m} of participants in that stage: Proposition 4. The unique risk dominant equilibrium is the PSE in which scientists in I* m participate in stage m, provided that for each consecutive pair of stages m and m’,
  • 29. Publishing partial results A researcher will publish partial results when •  When a stage is relatively valuable (Vm>Vm’) or easy (dm<dm’). •  When there are many competitors and/or competitors with high scientific capital •  When she has low scientific capital •  When the opportunity cost is low
  • 30. Example 2 An unknown disease strikes a dozen people in Louisiana, many of them golfers. It causes temporary paralysis and long-term joint pain. To take preventative action, we must solve a two-stage problem: 1)  What is causing this disease? 2)  And where is it coming from? Two teams, one from CDC, and one from LSU are well-poised to solve this mystery. Image:Alexander Putney, Sanskrit
  • 31. Louisiana golfer example CDC has capital 12 Values V1=V2=30 Difficulty D1=D2=15 LSU has capital 5 Fixed costs F1=4, F2=8 Opp. costs x=1 Only public sharing equilibrium in this game: Both CDC and LSU attempt stage 1. Whichever solves it first publishes immediately. Regardless of who solved stage 1, only CDC attempts stage 2 (and obviously publishes immediately.)
  • 32. Louisiana golfer example CDC has capital 12 Values V1=V2=30 Difficulty D1=D2=15 LSU has capital 5 Startup costs F1=4, F2=8 Opp. costs x=1 If researchers were not allowed to publish partial results: The only equilibrium has the CDC attempting the problem and LSU opting out. Here we see a partial publication norm recruiting increased effort to the problem.
  • 33. Social welfare (the “why it matters” part) In our model (as in life, largely) scientists are looking out for their own interests. How does this align with society’s interests? Because we model scientists’ outside options, we are in a position to consider this question explicitly.
  • 34. Social welfare Research creates knowledge, generating a (discounted) flow of value indefinitely onward into the future. Where K(t) is knowledge at time t, social welfare W is
  • 35. Social welfare Working on a hot problem interrupts daily progress, in exchange for a larger subsequent jump in knowledge when the hot problem is solved.
  • 36. Social welfare Where is the social value, is the social opportunity cost, and is the social cost of startup, the social welfare when scientists {1,2, …i} with total capital Hi work on the hot problem is Discounted Reward Cost of entry for i scientists Discounted opportunity cost
  • 37. Proposition 5. There is a unique social optimum, in which the ie scientists with the highest scientific capital work on the hot problem and the rest opt out.
  • 38. Social welfare results How does the risk dominant equilibrium (what scientists will do) compare with the socially optimum (what we would like them to do)? Both under-participation and over-participation are possible. Roughly (ignoring some subtle discounting terms) we see under-participation when
  • 39. Example 3 Halibut fisheries in Alaska abruptly collapse. This poses a two-stage problem: 1)  What is causing the collapse? Climate change? Disease? Overfishing? 2)  What can we do about it? Teams from NMFS and UW are able to attack the problem. Image:Alexander Putney, SanskritImage (cc) flickr: Steve Johnson
  • 40. Halibut fishery example NMFS has capital 10 Values V1=60 V2=30 Diff. D1=D2=15 UW has capital 6 Startup costs F1=1, F2=6 Opp. costs x=1 Value to society =100. Only public sharing equilibrium in this game: NMFS and UW attempt stage 1. Whichever solves it first publishes immediately. Regardless of who solved stage 1, only NMFS attempts stage 2 (and obviously publishes immediately.) Social welfare is W=122.94
  • 41. Halibut fishery example NMFS has capital 10 Values V1=60 V2=30 Diff. D1=D2=15 UW has capital 6 Startup costs F1=1, F2=6 Opp. costs x=1 Value to society =100. If we don’t allow partial progress sharing, both teams attempt the entire problem. In this case, the expected time to solution is shorter, and social welfare is higher W=126.98!
  • 42. Contrary to conventional wisdom, Proposition 6. Allowing partial progress sharing does not necessarily accelerate the rate at which a hot problem is solved. Why not?
  • 43. Monument to the conquerors of space (1964) Image:russianuniverse.org
  • 44. Future directions Problems of unknown difficulty –  Why scientists give up on a problem –  Strategic informational issues around non- publication. Reproducibility –  How do our institutions shape individual incentives in ways that contribute to or ameliorate the “reproducibility crisis.”
  • 45. Principal-agent framework –  How do alternative forms of credit allocation influence scientists’ behavior? –  What can a govt. agency do to shift scientists’ efforts toward the socially optimal allocation? –  How does the publishing system contribute to irreproducibility and inefficiency? –  How do within-university institutions accelerate or retard the progress of science? Policy implications and suggestions