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Summary of the entire unit 3 for introduction to game theory
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WHIT 3:MIXED STRATEGIESMixed Strategy:0 0, 02...3. K.Soi
~ =%
=
of player1 playing strategy 1
=
May introduce function
·
new IE+ the otherplayer's BR
change
~
Expected UtilityPayoffs:players playthe strategy thatgives them 4 Eutility.
1 playerplaying mixed:E(v2(0,1))
1. Foronly Payoff Payoff... Expected utility forplayer 2 if1 mixes
=
0. 0 2.
-
+
(
42 (01,52) G0n
=
v2 (51,52) ~Result:Payoff for1strategy (e juega pure
2. Ifboth mix:U2(01, 02) 027.
=
r2(02,527) +
O2 ve(O2, S2) -
...
fantas + como
strategies para 2 Maya
Expected
↓
payoffo fa mixed:smallerthan the largestpayofffrom a pure.
Result:Payoff forthe whole mixed game
~I ways to calculate payoffs expected value
1. 1stcalculate for Player1the payoffs he'd getifonlythe mixed
other (caso 1)
2nd each cell's found payoff.
multiply Player1's;o fplaying strategy.
that
v2(0e, 52) EO2".
=
v2 (81, s2K
2. Only calculation:foreach cell multiply:01.02 payoff the
of playeryou're doing his utility (caso 2)
U2(01, 02) S01.02.
=
Payoff (sumo tantas como celdas haya
~ Notation:Player1 :01= (p,1-p)
Player2:02 (p,
=
1 -
p)
BRAND NE
~
BR:ifvicoi, 0-i) >
vi (0'i, 0-i) 1. Calculo payoffs para Playerpara todas sus possibles strategies (caso 1)
2. Los comparoy the 4 me dice best strategyforthat player
3. Doypayoff del mixed Icaso 2) usando p
1 ex:find
Type of forwhat the BR change.
↓ p:if saldrauna strategy pure
When finding como BR
if payoff. Any mixed strategy is
ambas pure dan same BR
=
a
~Graph BRand
of ME:o 2 (p,1-p),
=
02 (q,1 p)
=
-
S12 is BR
E
E
in
⑦ Both are BR
NE
E -
e-
*
m
S1F BR
Player2 Player1
~
Expected payoff IE:
at elijo para cada playeru n a a calculada witp, py sustituyo p/p)todas dan mismo payoff)
~
Reaction function BR function =
(graph above (
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