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Summary of the entire unit 2 for Introduction to game theory.
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UNIT 2 -PURE STRATEGIES
IE, BR & PARETO for12 (nohax tabla)
Formulate
1. the game
·
Players 1 91, =
. .
.,
n}
·
Available Strategies:Si =93 for each i
Payoff
...
·
functions
0 if...
·
BRi)S-i):Whatshould i playin each situation
2. Analyze every situation:desde ambas perspectives (Si &s-i) miro si ambos BR. Ifyes, HE
3. From the found IE:Mito si podria alguno tenerofia BR. 3i nodStrictHE
4.
ForPareto:iqualy enlos casos donde yespE miro en cada situacion quien estavia worse off.
BELIEFS
~
People form beliefs aboutthe otherplayer's
possible strategy
~
Theirbeliefs are confirmed iff the BR the
of otherbased on his belief was yourbelief
IE:Belief profiles thatc an twin (the be confirmed)
~
outt o be correct & happen ones thatmay
~
StrictDE:beliefs thatwill be confirmed
RATIONALIZABILITY
~
Rationality:People BR to theirbeliefs
~
NEVER BR strategy is
A a NeverBR ifi t's a
not BR to any ofthe other's strategy profile
~
Finding the rationalizable profiles:Never BR method. ITERATED ELIMINATION (IERS)
1. Hago BR(*) en la tabla
2. Miro si alguna row (player1 payoffs) O columna (2's payoff) no tiene ninguna BR
3. Si nunca BR, tacho la row/c01.
4. con reduced table ruelvo a mirar.
! No -
c a n survive
HE
5. Rationalizable strategies:las que queda cuando no se puede in as
IE be
can't eliminated
1. Result:doesn'tdepend on the ordero felimination.
STRICT DOMII ANCE
1. A
strategyc a n be
~ Eliminates less strategies than rationalization.
strictly
not dominated bya ny other
strictlydominates strategyifall it's payoffs
~ Si another are
higher a neverBR
~
Strictly dominantstrategy:ifitstrictly
dominates all other strategies t he
of same player 3 1
~
IESD3:like IERS, but now I
go removing the strictly dominated strategies
1. Result:doesn'tdepend on the ordero felimination.
2
4
~
Dominance solvable game:ifafterIESDS only
1 strategy profile remains
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