E1EJI
PREFACE
Game theory shed s a light o n many aspect s o f the socia l sciences and i s based
on a n elegan t an d non-trivia l mathematica l theory . Th e bestowa l o f th e 1994
Nobel Priz e i n economic s upo n th e mathematicia n Joh n Nas h underscore s th e
important rol e thi s theor y ha s playe d i n th e intellectua l lif e o f th e twentiet h
century. Ther e ar e man y textbook s o n thi s topi c bu t the y ten d t o b e on e side d
in thei r approaches . Som e focu s o n th e application s an d glos s ove r th e mathe -
matical explanation s whil e others explai n th e mathematic s a t a leve l that make s
them inaccessibl e t o mos t non-mathematicians . Thi s monograp h fit s i n betwee n
these two alternatives. Man y example s ar e discussed an d completel y solve d wit h
tools tha t requir e n o mor e tha n hig h schoo l algebra . Thes e tool s tur n ou t t o b e
strong enoug h t o provid e proof s o f both vo n Neumann' s Minima x Theore m an d
the existenc e o f th e Nas h Equilibriu m i n th e 2 x 2 case . Th e reade r therefor e
gains both a sense of the rang e of applications an d a better understandin g o f th e
theoretical framewor k o f tw o dee p mathematica l concepts .
This boo k i s based o n lecture s I presented i n MAT H 105 Introductio n t o
Topics i n Mathematic s a s wel l a s i n MAT H 53 0 Mathematica l Model s
I a t th e Universit y o f Kansas . Th e first o f thes e course s i s normall y take n b y
Liberal Art s major s t o satisf y thei r Natura l Science s an d Mathematic s Distri -
bution Requirements . Th e presentatio n o f Chapter s 1-9 an d 11-1 3 i n thi s clas s
took abou t 2 5 lecture s an d wa s supplemente d wit h note s o n statistics , linea r
programming and/o r symmetry . I n th e mathematica l model s clas s thi s mate -
rial wa s use d t o supplemen t a standar d linea r programmin g course . I t ca n b e
covered i n abou t a doze n lecture s wit h proof s include d i n bot h th e presentatio n
and th e homewor k assignments . Thos e chapter s an d exercise s tha t ar e deeme d
to b e mor e theoreticall y demandin g ar e starred . Suc h proof s a s ar e include d i n
the tex t appea r i n th e conclusio n o f the appropriat e chapters .
The exposition i s gentle becaus e it requires only some knowledge of coordinat e
geometry, an d linea r programmin g i s not used . I t i s mathematical becaus e i t
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