Summary topic 5 and 6

SEQUENTIAL GAMES

SEQUENTIAL GAMES WITH PERFECTINFORMATION

~
Sequential game:players don'tplay simultaneouslybutone afterthe other. Payoffs given once the
at end ofthe
game.
With perfectinformation:players know pointall previous actions
·




any
at the taken

·



Described by:(N. Ai, 'game tree', ui) (Actions available to iatnonterminal nodes]

Representation:Game tree 1. terminal nodes:nodes where ends [levan payoffs]
·




game
Notation:
2. Decision nodes:a l l the othernodes.
X.Y to tell which t he
of playerX decision node itis.
-which Player (1,2)
3. Chance nodes:puede estar o no al principio del tree."Nature &
moves 1st decides who moves 1st.

~
Subgame:Part game of from a decision/chance node to the end. I
subgame per decision node.!Main game:also a
subcame.
Length:longestpath from the root (decision node selected) to a terminal node. (max ri d ecisions
of h ave to
that be madel.
Total subgames
ri of ri
=
ofdecision nodes


~
Strategy:Specification t he
of actions t he
of
playerforeach his
of nodes. 1
strategy lo que ha decidido
jugaren cada uno de sus nodes).

Contingentstrategy:Una strategyimpossible. (1.1: T, 1.2:Take) I f1.1= T the ends & 1.2 can'tbe played
game
1. included! (todas han de considerar nodes!)
Contingent ones las
strategies a todos los


~
1. Extensive form:
Representing a
game game tree. To representsequential move
games. Maybe you need to

2. Normal fork matrix. To represents imultaneous Combine both!
move
games.
:




game

1. From extensive to normal form (perfect]
1. Miro cuantas opciones tiene cada las multiplico - Result n cells
=




player + of



2. Hago tabla con payoffs para cada
strategy (including contingentones (
NEof
↓
table can be a BIE not!
or 1 NE ser SPNE, el otro no seraposible! (successfull butnotcredible threat]


BR & NE


1.NE:hago tabla con los payoffs ymiro. Notsuitable to decide in sequential

~
BIE:finds best
strategies assuming in prior
stages we maximize the payoffs (SPE) (no one can do betterin any
subcame than the marked strategies).
subgames (mirando payoffs decide). Resulting path:BIE=SPE [e- a equilibrium path] =




1. Mark for 1
BR length del playerque
2. payoffs Player's strategy:digo el marcado para cada node
Mark now
length
for 2
looking t he
at marked

rooto fmain
·Outcome:BIE payoff
3. Repeatuntil you reach game
~
Subgame PerfectN ash Equilibrium:Strategy profile where in
everysubgame players can'tdo betterby
changing their
strategy.
·
coincides with BIE in Sep. With perfect!All SPE NE (not riceversa!)
·

coincides with NE in simultaneous games!Forboth perfect & imperfects eq




SEQUENTIAL GAMES WITH IMPERFECTINFORMATION

~
Sequential game Withimperfectinformation:there are hidden actions & a playercan'tknow atthat
stage on which node he is.
·

Representation:dotted line between the nodes thatcome afterthe hidden action

~ Information set:this seto fdecision nodes that1. Belong to the same player "frain only
varios
·
como un
subgame que engloba subgames 2. Have the same available actions (son iguales sus
subjames) contains 1 decision
n ode


~
Strategy:complete contingentplan specifying an
action areaitisriseassetsdeducenasoptionsenlatabia!
1. From extensive to normal form [imperfect]:igual que perfectpero despues de dotted line solo
pongo
1 vez en la tabla las options.




-
4
subgames
n'of "teenode
n of decision nodes