games, groups, norms and societies · 1 day ago · “raiffa opted to cover 2-person games and...
TRANSCRIPT
![Page 1: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/1.jpg)
Games, Groups, Norms andSocieties
Simon Levin, UCI 2008 http://www.n-line.co.uk/2006/04/18/china_traffic/
![Page 2: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/2.jpg)
• We are here to honor a classic text
![Page 3: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/3.jpg)
Games and DecisionsIntroduction and Critical Survey
Luce and Raiffa
![Page 4: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/4.jpg)
“Raiffa opted to cover 2-persongames and statistical decision
theory, and I focused on n-persongames…and information theory”
Duncan Luce, 1988
![Page 5: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/5.jpg)
Unique challenges
•• Collective dynamicsCollective dynamics–– Relation between individuals and groupsRelation between individuals and groups
•• Multiple scalesMultiple scales–– Dynamic of norms and societiesDynamic of norms and societies
•• Behavior/ecology and evolutionBehavior/ecology and evolution–– What should individuals do?What should individuals do?
•• Proximate Proximate vsvs. ultimate explanations. ultimate explanations
![Page 6: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/6.jpg)
A fundamental insight ofA fundamental insight ofevolutionary theory is thatevolutionary theory is that
ultimate and proximateultimate and proximateexplanations need not coincideexplanations need not coincide
![Page 7: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/7.jpg)
Evolutionary biology
• Proximate vs. ultimate cause
www.waynesthisandthat.com
![Page 8: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/8.jpg)
• Initial reasons for pattern may simplyprovide template for evolution of adaptation
![Page 9: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/9.jpg)
Such observations hold forgroups
• Initial reasons for aggregation may simply providetemplate for evolution of adaptive behavior
www.wildcrest.com/Frantz/
![Page 10: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/10.jpg)
www.birminghamzoo.com
![Page 11: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/11.jpg)
Pattern formation
•• Symmetry breakingSymmetry breaking•• Reinforcement and stabilizationReinforcement and stabilization
![Page 12: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/12.jpg)
www.nature.ca/notebooks
![Page 13: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/13.jpg)
Formation of societies
•• Random associationsRandom associations•• Active aggregationActive aggregation•• Stabilization of group boundariesStabilization of group boundaries•• Customs, norms, lawsCustoms, norms, laws•• Institutions, religions, societiesInstitutions, religions, societies
![Page 14: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/14.jpg)
Even phytoplanktonare patchily distributed
spiff.ucsd.edu
![Page 15: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/15.jpg)
Random inhomogeneities lead to reinforcement:Attraction and repulsion in gregarious animals
Tony Sinclair
![Page 16: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/16.jpg)
AnimalAnimal groupsgroups like this bird flock emergelike this bird flock emerge from from individuals following local rulesindividuals following local rules
![Page 17: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/17.jpg)
What is the relationship betweenan individual agent
![Page 18: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/18.jpg)
...and how it responds to itsneighbors and local environment
![Page 19: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/19.jpg)
......and the macroscopic properties of ensembles of such agents?and the macroscopic properties of ensembles of such agents?
![Page 20: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/20.jpg)
How do individuals learn therules, the social norms?
•• Non-human animal groupsNon-human animal groups•• Beijing trafficBeijing traffic•• SocietiesSocieties
![Page 21: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/21.jpg)
Games and collective search
Grunbaum
![Page 22: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/22.jpg)
There is a long and rich history ofthe application of mathematics to
ecology
Vito Volterra 1860-1940
Fluctuations of the Adriatic Fisheries
![Page 23: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/23.jpg)
VariantsVariants on on VolterraVolterra’’s s original equationsoriginal equationsexhibit robust limit-cycle behaviorexhibit robust limit-cycle behavior
!
dx /dt = a(x,y)x(t)
dy /dt = b(x,y)y(t)
www.vanderbilt.edu/AnS
![Page 24: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/24.jpg)
Evolutionary theory also has a rich mathematical historyEvolutionary theory also has a rich mathematical history
R.A.FisherR.A.Fisher J.B.S.J.B.S.HaldaneHaldaneSewall Sewall WrightWright
![Page 25: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/25.jpg)
The challenge remains to meldthese two scales
Place ecological interactions withinPlace ecological interactions withinan evolutionary frameworkan evolutionary framework
!
dx /dt = f (x;",E)
d" /dt = #g(x;",E)
To do so, must embed this systemTo do so, must embed this system in an even higher-order system in an even higher-order system
Ecological
Evolutionary
Fast scale:
Slow scale:
![Page 26: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/26.jpg)
Approaches to marrying ecologyand evolution
•• OptimizationOptimization•• Game TheoryGame Theory•• CoevolutionCoevolution
–– TightTight–– DiffuseDiffuse
www.dkimages.com
![Page 27: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/27.jpg)
Evolution and the Theory ofEvolution and the Theory ofGamesGames
““Evolution is an existentialist gameEvolution is an existentialist game””
LBSlobodkin
![Page 28: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/28.jpg)
Darwin saw natural selection as aprocess of gradualgradual adaptation in a
changing environment
www.biology-online.org
![Page 29: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/29.jpg)
Too easily, however, thistransmogrified into
Evolution as optimizationEvolution as optimization
www.thehitsdoctor.com
![Page 30: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/30.jpg)
Why Optimization?
FisherFisher’’s fundamental theorems fundamental theoremof natural selection:of natural selection:
The mean fitness will increaseThe mean fitness will increasetowards a maximum.towards a maximum.
![Page 31: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/31.jpg)
Selection as hill-climbing findsmaxima
Hence, an optimization principle emergesHence, an optimization principle emerges
!
dw /dt = s(pq /w )(dw /dp)2
!
w
![Page 32: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/32.jpg)
•• Genetic constraints (epistasis, linkage)Genetic constraints (epistasis, linkage)•• Temporal change in the landscapeTemporal change in the landscape•• Frequency dependenceFrequency dependence•• CoevolutionCoevolution
But there are problems with thisseductive picture
Indeed,Indeed,
![Page 33: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/33.jpg)
The deepest problems involvefrequency-dependencefrequency-dependence and
coevolutioncoevolution
encyclopedia.laborlawtalk.com
![Page 34: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/34.jpg)
Because of coevolution andfrequency-dependence
•• Optimization must give way to game theoryOptimization must give way to game theory
![Page 35: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/35.jpg)
To deal with this,To deal with this,Maynard Smith introduced the game-theoreticMaynard Smith introduced the game-theoretic
notion of the evolutionarily stable strategy (ESS): notion of the evolutionarily stable strategy (ESS):
www.pbs.org
A strategy that, once established,A strategy that, once established, cannot be invadedcannot be invaded
![Page 36: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/36.jpg)
Things become more complicated ifwe study the dynamics of such games
and how strategies changehttp://www-eco.enst-bretagne.fr/~phan
![Page 37: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/37.jpg)
Modified Hawks vs. Doves
Maynard SmithMaynard Smith
![Page 38: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/38.jpg)
Case 3:
[ ] -0.6 0.9 -0.9 0.7
![Page 39: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/39.jpg)
Hawks and Doves
Durrett and Levin,1994/Buttel/Case 3
![Page 40: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/40.jpg)
Spatially restricted competitionSpatially restricted competition
•• Hawks Hawks outcompeteoutcompetedoves locallydoves locally
•• Then hawks go extinctThen hawks go extinctlocallylocally
•• Doves Doves recolonize recolonize emptyemptyareasareas
![Page 41: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/41.jpg)
In this example, viscosity iscrucial
But anomalies also can arise without itBut anomalies also can arise without it
![Page 42: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/42.jpg)
Evolutionary dynamics ofphenotypes
•• r(v,u) is the fitness of a rare phenotype v invading ar(v,u) is the fitness of a rare phenotype v invading apopulation in which u is establishedpopulation in which u is established
•• r(v,u) typically is the linearized growth rate of the v-r(v,u) typically is the linearized growth rate of the v-phenotype population near (0, u*)phenotype population near (0, u*)
•• More generally, dominant eigenvalue or Floquet exponentMore generally, dominant eigenvalue or Floquet exponent
Henceforth, assume scalar phenotypesHenceforth, assume scalar phenotypes
![Page 43: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/43.jpg)
The fitness surface is now dynamic
!
w
![Page 44: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/44.jpg)
Focus just on invasion dynamicsat critical points
Piotr Zacny
![Page 45: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/45.jpg)
Resident u
Invader vConvergence-stable
u=vr=0
!
"r /"u+ "r /"v = 0
So critical points with respect to u and v coincide on diagonal
![Page 46: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/46.jpg)
ESS (evolutionarily stable strategy)
r r ((vv, , uu) is maximized as a function of ) is maximized as a function of vv at at v v == u u
!
"r
"v=0,
" 2r
"v 2# 0
uu
![Page 47: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/47.jpg)
But the notion of ESS turns outto be just a beginning
•• There may be several ESSesThere may be several ESSes•• ESS may not be reachableESS may not be reachable
![Page 48: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/48.jpg)
Need complementary notions
•• Neighborhood invader strategyNeighborhood invader strategy•• Convergence stable strategyConvergence stable strategy
![Page 49: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/49.jpg)
Resident u
Invader vConvergence-stable
u=vr=0
!
"r /"v > 0
A resident to the left can be invaded from the right
![Page 50: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/50.jpg)
Resident u
Invader vConvergence-stable
r=0
!
"r /"v # 0
!
"r /"v # 0
A resident to the right can be invaded from the left
![Page 51: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/51.jpg)
Resident u
Invader vConvergence-stable
r=0
!
"r /"v # 0
!
"r /"v # 0
!
" 2r /"u"v +" 2r /"v 2 # 0
!
"r /"v = 0
Or, equivalentlyOr, equivalently
![Page 52: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/52.jpg)
Convergence-stable strategy
!2r
!v2"!
2r
!u2
(attracting in space of phenotypes)(attracting in space of phenotypes)
Hence, an ESS may not be attracting
And an attracting strategy may not be an ESS
![Page 53: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/53.jpg)
This leads to a powerful way tounderstand observed strategies
•• Begin with a basic dynamical modelBegin with a basic dynamical model•• Allow (heritable) variation in the traits of interactingAllow (heritable) variation in the traits of interacting
individualsindividuals•• Explore the adaptive dynamics of such systems, includingExplore the adaptive dynamics of such systems, including
–– continuously stable strategies (convergence-stable continuously stable strategies (convergence-stable ESSesESSes))–– evolutionary branching and possibleevolutionary branching and possible–– coexistence of typescoexistence of types
![Page 54: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/54.jpg)
The evolution of altruism andcooperation
•• AltruismAltruism was a puzzle for Darwin
www.csiro.au
![Page 55: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/55.jpg)
Even bacteria cooperate
www.cs.montana.edu/~ross
![Page 56: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/56.jpg)
Link between group living and communication
Quorum Sensing Slime Biofilms
Low cell density High cell density
Pseudomonas aeruginosa Slime OFF Slime ON
Vibrio cholerae Slime ON Slime OFF
Extracellular Polymers (Slime)
Key
Cell that makespolymer
Cell that cannotmake polymer
Extracellularpolymer
Nutrient Diffusion
Nadell, Xavier, Levin, Foster
![Page 57: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/57.jpg)
Biofilm formation and quorum sensing
Constitutive Slime-producer
Slime
QS Strain (below quorum)
QS Strain (above quorum)
Nadell, Xavier, Levin, Foster
![Page 58: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/58.jpg)
WhatWhat’’s happening?s happening?
![Page 59: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/59.jpg)
Similar ideas may be applied toother animals
• Slime molds• Insects• Krill• Birds• Fish•• UngulatesUngulates
Couzin
![Page 60: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/60.jpg)
Fundamental questions
•• How are individual decisions affected byHow are individual decisions affected bythe social context?the social context?
•• How does the social context emerge andHow does the social context emerge andevolve?evolve?
![Page 61: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/61.jpg)
Issues
•• ExploExploration ration vsvs. Exploitation. Exploitation•• DiscountingDiscounting•• Costs/benefits of leadershipCosts/benefits of leadership•• Group sizeGroup size
![Page 62: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/62.jpg)
Group membership providesbenefits, to some extent in
competition with other groups
www.sit.edu
![Page 63: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/63.jpg)
Group membership providesadvantages over being solitaryBut those benefits may decrease as group size increases
http://humwww.ucsc.edu/gruesz/war/scene.jpg
![Page 64: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/64.jpg)
In many animal species, individualsassemble themselves into
aggregations
www.public.iastate.edu/~jhale
![Page 65: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/65.jpg)
Macroscopic patterns emergewhen individuals follow one
another…among humans
web-japan.org
![Page 66: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/66.jpg)
…as well as other animals
www.nomadafricantravel.co.uk
![Page 67: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/67.jpg)
…leading to fascinatinggeometries
www.travellersworldwide.com
![Page 68: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/68.jpg)
www.pigeon.psy.tufts.edu
Individuals imitate othersIndividuals imitate others’’ behavior behavior
![Page 69: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/69.jpg)
And fads and customs proliferate
www.tattoobyshad.com
![Page 70: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/70.jpg)
…uniformity prevails
![Page 71: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/71.jpg)
Formation of societies
•• Random associationsRandom associations•• Active aggregationActive aggregation•• Stabilization of group boundariesStabilization of group boundaries•• Customs, norms, lawsCustoms, norms, laws•• Institutions, religions, societiesInstitutions, religions, societies
![Page 72: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/72.jpg)
• Simple memes: Threshold voter modelSimple memes: Threshold voter model (the traditional,oversimplified fare)
Problems of scale
![Page 73: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/73.jpg)
• Simple memes (the traditional,oversimplified fare)
• Clusters of memesClusters of memes (traits or behaviors are not independent)
Problems of scale
![Page 74: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/74.jpg)
24857
13657
Focalindividual
Neighbor
Labels
Social norms, multiple traits/opinions Durrett and Levin, JEBO
*Religion*Religion*Ethnicity*Ethnicity*Political party*Political party
Related to a model of Axelrod
![Page 75: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/75.jpg)
24857
13657
Focalindividual
Neighbor
Labels Attitudes
Social norms, multiple traits/opinions
*Abortion rights*Abortion rights*Stem-cell research*Stem-cell research*Gay marriage*Gay marriage
![Page 76: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/76.jpg)
Homophilous Homophilous ImitationImitation
Analogies to Schelling’s model
![Page 77: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/77.jpg)
Formation of cooperative groups
•• Imitation alone can lead to formation ofImitation alone can lead to formation ofstable groupsstable groups
![Page 78: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/78.jpg)
Formation of cooperative groups
• Imitation alone can lead to formation ofstable groups–– Opinions and attitudes on diverse issues mayOpinions and attitudes on diverse issues may
get bundled as get bundled as ““frozen accidentsfrozen accidents””
![Page 79: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/79.jpg)
Formation of cooperative groups
• Imitation alone can lead to formation ofstable groups
•• Existence of groups can produce collectiveExistence of groups can produce collectivebenefitsbenefits
![Page 80: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/80.jpg)
Formation of societies
•• Random associationsRandom associations•• Active aggregationActive aggregation•• Stabilization of group boundariesStabilization of group boundaries•• Customs, norms, lawsCustoms, norms, laws•• Institutions, religions, societiesInstitutions, religions, societies
![Page 81: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/81.jpg)
Formation of cooperative groups
• Imitation alone can lead to formation ofstable groups
• Existence of groups can produce collectivebenefits
•• Collective benefits can lead to selection forCollective benefits can lead to selection forimitation, higher thresholdsimitation, higher thresholds
![Page 82: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/82.jpg)
Extensions
• More complex webs of interaction (smallworlds)
• Asymmetric imitation•• Power structurePower structure
![Page 83: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/83.jpg)
Extensions
• More complex webs of interaction (smallworlds)
• Asymmetric imitation• Power structure•• Payoffs (Fitness differences)Payoffs (Fitness differences)
![Page 84: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/84.jpg)
Role of leadershipCouzinCouzin,, Franks, Krause, LevinFranks, Krause, Levin
![Page 85: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/85.jpg)
g1
Col
lect
ive
deci
sion
-mak
ing
Trend setter
Copier
![Page 86: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/86.jpg)
So the direction chosen by informed individuals mustreconcile these tendencies.
si(t)
di(t+Δt) = si(t) + ω gi(t)si(t) + ω gi(t)
Col
lect
ive
deci
sion
-mak
ing
gi(t)
![Page 87: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/87.jpg)
1 informed individuals in group of 100.
Col
lect
ive
deci
sion
-mak
ing
![Page 88: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/88.jpg)
10 informed individuals in group of 100.
Col
lect
ive
deci
sion
-mak
ing
![Page 89: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/89.jpg)
Animal groups may be led by asmall number of individuals
![Page 90: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/90.jpg)
Difference in preference
Col
lect
ive
deci
sion
-mak
ing
Competing preferencesCompeting preferences
![Page 91: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/91.jpg)
0 20 40 60 80 100 120 140 160 180
0
30
60
90
120
150
180
210
240
270
300
330-120
-150
180
150
120
90
60
30
0
-30
-60
-90
0 20 40 60 80 100 120 140 160 180
0
30
60
90
120
150
180
210
240
270
300
330-120
-150
180
150
120
90
60
30
0
-30
-60
-90
-120
-150
180
150
120
90
60
30
0
-30
-60
-90
Difference in preference
Col
lect
ive
deci
sion
-mak
ing
![Page 92: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/92.jpg)
Leadership
•• Influence of leadershipInfluence of leadership•• Emergence of leadershipEmergence of leadership
![Page 93: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/93.jpg)
g1
Col
lect
ive
deci
sion
-mak
ing
Why do individuals use particular strategies?Why do individuals use particular strategies?
![Page 94: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/94.jpg)
How does selection shape the trade-off between trackingHow does selection shape the trade-off between tracking resources and tracking other individuals?resources and tracking other individuals?
What is the value of information?What is the value of information?
![Page 95: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/95.jpg)
Can this be extended to dynamicsin abstract opinion spaces?
What determines who the leaders are?What determines who the leaders are?
![Page 96: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/96.jpg)
• Simple memesSimple memes
(the traditional,oversimplified fare)(the traditional,oversimplified fare)
•• Clusters of memes Clusters of memes
(traits or behaviors are not independent)(traits or behaviors are not independent)
•• Systems of justice, morality Systems of justice, morality
(collective dynamics of whole systems exhibit unique emergent(collective dynamics of whole systems exhibit unique emergentproperties)properties)
Problems of scale
![Page 97: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/97.jpg)
Many social norms can only beunderstood in broader contexts than those
in which they are observed
•• Charitable givingCharitable giving•• Ultimatum gameUltimatum game•• Fehr Fehr experimentsexperiments
![Page 98: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/98.jpg)
Broader questions
•• How do groups become stabilized?How do groups become stabilized?•• Political parties (Political parties (DuvergerDuverger’’s s law)law)•• ReligionsReligions•• SocietiesSocieties•• LawsLaws•• Problems of the Global CommonsProblems of the Global Commons
![Page 99: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/99.jpg)
Need expanded game-theoreticframework
•• Rewards for adherence to group normsRewards for adherence to group norms•• Historical effectsHistorical effects•• Meta-game contextMeta-game context•• HeuristicsHeuristics•• Multiple scales, in which group dynamicsMultiple scales, in which group dynamics
consideredconsidered
www.dentsply.ca
![Page 100: Games, Groups, Norms and Societies · 1 day ago · “Raiffa opted to cover 2-person games and statistical decision theory, and I focused on n-person games…and information theory”](https://reader036.vdocuments.us/reader036/viewer/2022070903/5f61929809afbb5cb83ad167/html5/thumbnails/100.jpg)
I hope to have this worked out forthe 60th anniversary
Thank you Thank you