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30DUL-
8
-
Gametheory:Study of strategic Interactions Interactionbetween 2+ & theychoose strategies thatlead payoffs.
-
to
~ players
· Decision theory:Same but
single-agent
·
key ingredients:1. players (11)
2. Actions (Ail belong to IR
the 4 the better
3. Payoffs (ui):outcomes:Aix...
depend on actions made by players
· The tragedy of the commons
f
·
cooperative outcome a collective decision, we'll obtain the f(x)
maximum= c'(x)
=
=average h ow
of much produced per x
·
Non-cooperative outcome. Individual decision. Solution b een discussed.
hasn't I to make it, we look for1 x
cx c o st
=
1x.
of
derivative
marginal cost
=
. . .0 - - - -
derivative
marginal production
NASH EQUILIBRIUM
~ Ifeach player's strategy
is a BR) *
marked fora l l sil
~
StrictHash Equilibrium:i feach strategy is the only BR (Pla er1 no tienemas * enesa columna, Player 2 tampoco en esafilal.
~ HEwhere bothBR(*)
Finding a mask equilibrium:I find all BR forall players.
~
There can be 1, Several orn o IE.
~
IEcan be
not Pareto & viceversa.
BEST RESPONSE
~
Bestaction fora playerifhe knew the other's actions
~
1 BR leastforeach
at the
of other's strategy (si 2 tienen mismo payoffM arco las 2)
PARETTO EFFICIENCY
~It's paretto ifchanging to any otherstrategy profile worsens atleast1 player(smaller payoff), or
gives exactly
the
same payoffs (si ambas son iquales son Pareto).
PREFERENCES
~
Complete:You can
give an answerevenfor weakpreferences
Strong:x > Y
I you can chouse ifx yo ry x ) ~
ifboth fulfilled - utilityfunction can be made
weak:x y
·
Transitive:L a cadena secumple. xy& yz
+
x >, z
Indifferent:x my
weak includes u
&x y implies y
x
UICERTAIN ITY
(0) ProbabilityOn, 02... On
States
P1, P2...PM pi c,0&Spi=1:a l l possible situations are covered
~consequences/
. Pay o f S
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