Mdli dR i lAlt iModeling and Reciprocal Altruism

20 Pages·2007·0.58 MB·English

MModdelliing andd RReciiprocall AAllttruiism
TThhee  uussee  ooff  ggaammee  tthheeoorreettiicc  
simulation as a way to model 
rreecciipprrooccaall  aallttrruuiissmm
AA fformall ddeffiiniittiion off a moddell
An abstract model (or conceptual model) is a theoretical
construct that represents something, with a set of variables
and a set of loggical or qquantitative relationshipps between
them. Models in this sense are constructed to enable
reasoning within an idealized logical framework about
these processes and are an important component of
scientiffic thheories. Iddeallizeddhhere means thhat thhe moddell
may make explicit assumptions that are known to be false
(or incomplete) in some detail. Such assumptions may be
jjuussttiiffiieedd oonn tthhee ggrroouunnddss tthhaatt tthheeyy ssiimmpplliiffyy tthhee mmooddeell wwhhiillee,
at the same time, allowing the production of acceptably
accurate solutions, as is illustrated below.
The Use of Models
Models are useful when there is some
undderstanddiing off thhe probbllem, bbut iiddeas abbout
how to analyze the data are limited.
Models help
•define the pproblem
•organize thought about the problem
•understand data
•test understanding
•make further ppredictions
Procedures for Modeling:
Begin with the simplest model or one that has
fewest assumptions and the fewest variables for
tthhe ffollllowiing reasons:
•Few assumptions allows the model to be more
ggeenneerraall, oorr ccoovveerr aa ggrreeaatteerr nnuummbbeerr ooff ccaasseess
(e.g., players do not have to be rational,
tthheeyy ssiimmppllyy ffoollllooww rruulleess ooff tthhuummbb))..
•If a model with few variables is moderately
successful then more variables can be
added to make it more precise and realistic
(if complex models fail it is difficult to
determine which variable is problematic).
TThhee MMooddeelleerr''ss DDiilleemmmmaa
MMooddeellss ccaannnnoott ssiimmuullttaanneeoouussllyy mmaaxxiimmiizzee
the following important qualities
:
precision (make accurate predictions)
generality ((apply to a large number off cases))
realism ((cappture all the variables that
determine the outcome)
Thee Baassicc Proobbleem:
How can cooperation evolve in a world of egoists
unconsttraiinedd bby a centtrall autthhoriitty?? SSuchh a siittuattiion
assumes that individuals are selfish or have an incentive to be
selfish. Answering this question will allow us to specify the
conditions under which reciprocal altruism can evolve.
“TThhee pprriissoonneerr'ss ddiilleemmmmaa iiss ssiimmppllyy aann aabbssttrraacctt ffoorrmmuullaattiioonn ooff
some very common and interesting situations in which what is
best for each person individually leads to mutual defection,
whhereas everyone woulldd hhave bbeen bbetttter offff wiitthh muttuall
cooperation.”
P. 9 The Evolution of Cooperation, R. Axelrod
TThhe PPriisoner’’s DDiillemma
The basic idea is that if you are a prisoner planning to
escape with some fellow prisoners. You have the choice of
bbeeiinngg ffaaiitthhffuull ttoo tthheemm aanndd bbeenneeffiittiinngg ffrroomm tthheeiirr ppllaann, oorr yyoouu
can betray them and earn what may be a very considerable
reward from the authorities. You also must consider that this
choice will have occurred to the others, which means that
you stand in danger of special retribution if you are betrayed
first. This kind of pproblem can be abstracted into a little ggame
and an associated payoff matrix.
TThhee PPrriissoonneerr’’ss DDiilleemmmmaa PPaayyooffff
MMaattrriixx
Column Player
Cooperate Defect
R=3, R=3 S=0, T=5
Reward for Sucker's payoff
Cooperate
MMuuttuuaall aanndd tteemmppttaattiioonn ttoo
cooperation defect
Row
pplaayyeer
T=5, S=0
P=1, P=1
Temptation to
Defect Punishment for
defect and
mutual defection
ssuucckkeerr''ss ppaayyooffff
If the only winning strategy is to defect,
how can cooperation emerge?
The only way in which cooperation can
(cid:132)
emergge is if there will be future
interactions.
TThhaatt iiss,, tthhee ggaammee wwiillll bbee ppllaayyeedd aaggaaiinn aanndd
(cid:132)(cid:132)
again.
TThhee ggrreeaatteerr tthhee nnuummbbeerr ooff iitteerraattiioonnss tthhee
(cid:132)(cid:132)
more likely cooperation will evolve
Best Strategy (more or less):
TTiitt-ffor-ttatt
Tit-for-tat is based on a simple algorithm:
(cid:132)
Coopperate on first meetingg
(cid:132)
Do what ever your opponent did to you in the
(cid:132)
last round
Other strategies do well under other
(cid:132)
ccoonnddiittiioonnss
Win, stay; loose, shift (a simple Pavlovian
(cid:132)
model))