STAT 155 Study Guide - Fall 2018, Comprehensive Midterm Notes - Xz, Nim, If And Only If
STAT 155
MIDTERM EXAM
STUDY GUIDE
Fall 2018
Stats 155 OH :2:15 -4:i5 Shirshendn
Game theory Alive ,Karlin Peres
!1!Analysis of game
!2!Design
a) Combinatorial games
b) zero -sum games
c) general -sum games (Nash -quuilibrio )
d) correlated equilibria ,evolutionary
e) price of anarchy
!2!a) co -operative games
b) voting
c) Auctions
d) stable Matching
Combinatorial games
!1!Subtraction games
A. B2players 11=15 /#of chips
Both the players already remove 1or 2chips ,
Player removing the last Chip wins (Normal Play )
X=l I
X=2 I
X=3 I
X=4 I
what is general strageey
X=3K 11=3*3142
Iplayer has awinning Strategy
find more resources at oneclass.com
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X=3k no matter what 1does
It has awinning strategy ?
Progressively bounded games
Sis the set of States
Tcs
be the set of terminal States
Strategy :Impartial games
I,Ihas the same set of
legal moves
MIC SXS
x→y
(x,Y)EMI if Iis allowed to move
to yfrom ×
Agame is progressively bounded if started from
any xt sthere is anumber nsuch that all
games last at most nrows
strategy for 1sample for S->sst for an xes
(X,FCX ))
Eµ1=*
well 342
See next class s= PUN →nex
all States where previous Player wins
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Combinatorial games games equilibria ( nash quuilibrio ) , evolutionary sum zero b: general d) correlated games sum, price. !2! a) co - of anarchy games operative: voting c) S is bounded set of be the games. I games the same set of legal moves. I is allowed to move is progressively xt s last there at is most a n bounded number rows if n started from such that all for. S - > s st for an xes to. X x 1 set of legal element of. M , an from y players alternately choosing to is ( x some. X s op last player to move wins lh=m2 lhtnu from which there is no move suppose i starts at r r. V 9 . r q r q - forever. Start on the from x . progressively bounded games. Xs c- x of steps of acyclic are number.
