Lid
INTRODUCTIO N
The notio n o f a zero-su m gam e i s informall y introduce d an d
several example s ar e discussed .
The mathematica l theor y o f game s wa s first develope d a s a mode l fo r situation s
of conflict . I t gaine d widesprea d recognitio n i n th e earl y 1940's whe n i t wa s
applied t o th e theoretica l stud y o f economic s b y th e mathematicia n Joh n vo n
Neumann an d th e economis t Oska r Morgenster n i n their boo k Theory of Games
and Economic Behavior. Sinc e then it s scop e has bee n broadene d t o includ e co -
operative interactions as well and i t has been applied to the theoretical aspect s of
many o f the social sciences. Whil e the jury i s still out o n the question o f whethe r
this theor y furnishe s an y valuabl e informatio n regardin g practica l situations , i t
has stimulate d muc h basi c researc h i n discipline s suc h a s economics , politica l
science, an d psychology .
Situations o f conflict , o r an y othe r kin d o f interactions , will b e calle d games
and the y have , b y definition , participant s wh o ar e calle d players. W e shall limi t
our attentio n t o scenario s wher e ther e ar e onl y tw o player s an d the y wil l b e
called Rut h an d Charlie . Th e existenc e o f a conflic t i s usuall y du e bot h t o
the desir e o f eac h playe r t o improv e hi s circumstances , frequentl y b y mean s o f
some acquisition , an d th e unfortunat e limite d natur e o f al l resources . Fo r al l
but th e las t thre e chapter s o f thi s boo k i t wil l b e assume d tha t eac h playe r i s
striving to gain as much a s possible, an d tha t eac h player's gain is his opponent' s
loss. Finally , eac h playe r i s assumed t o hav e several options o r strategies tha t h e
can exercis e (on e a t a time ) a s hi s attemp t t o clai m a portio n o f th e resources .
Because of the introductory natur e of this text, mos t of the subsequent discussio n
is restricte d t o situation s wherei n th e player s mak e thei r move s simultaneousl y
and independentl y o f eac h other . I t wil l b e argue d i n Chapte r 10 tha t thi s
does no t trul y limi t th e scop e o f th e theor y an d tha t th e mathematica l theor y
http://dx.doi.org/10.1090/mawrld/013/01
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