Summary

TOPICY:ZERO SUM GAMES
SECURE PAYOFF

~Worst payoff fora playerin each possible strategy (el que seguro que
gana da igual lo que juegue el otto


~
IEFSecure Payoff!




MAXMINIMIZATION
INPURE


~WorstPayoff:Wi(Si) minvi(si,sj):si escoge strategy Si, =

al menos recibe wi(si) daigual 5; delotro.


~
Pure Maxmin/Security Strategy:gives the playerthe besto fthe c ases:Max
worst Wilsi) Security Payoff
=




Finding it:Mirotabla Marco cada
·

1. menor payoff en strategy.

2. El dice la security strategy.
+
de esos me



MIXED STRATEGIES

~
(Ki-1) -


Simplex:Seto fmixed strategies of playeri 8;
2- simplex (3 points)
1

1. SimpleX
simplex:2 strategies & line is strategies (0, )


z
Ex:1 -

·




mixture t he 2.
⑧ ·
that
are a of

I i
·




2- simple
siz
5;3
MAXMINIMIZATION
INMIXED


~Wiloil:lowestexpected payoff Ican getifchoosing mixed strategy oi (da igual lo que el otro, al menos se lleva wiloi))

Wi(vi) minvi(8i,5j)
=




~
Security Strategy (5i):M a x Wicoi):gives security
payoff

·


Finding it:1. I find worst payoff foreach the
of other's pure strategy.


2. Igualo las 2ecuaciones para encontraro que define 01 (01,1
=
-

01)
cual es el payoff
worst
W1(01) min[vi(81, ),
=

vi(01, B73
3. I find security payoff:sustituyo o en 1 de las 2 y lo que de




Graphically (graph forplayer1)


2 lines:van de 0 0
=


a 0 1
=




~ Eno
=


0: cadalineasale del Payoff B (1
= -
0)


~ En =1 :Marco Payoffs A
=
0



Intersection:Maxmin o & security payoff (y axis)

- -




Security Strategy:el valor Value t he
of
game:security
payoff of
player1

de o encontrado. 0 (0,1 0)
=
-
V V1
= = -

V2


Cuando descubro o, sustituyo en 1 de las eps y me



da V.