CSC 5350 Assignment 2
Due date: 9 November 2008
1.
Subgame perfect equilibrium can be defined using the one deviation
property if the game has finite horizon.
Show that this property does not
hold for infinite horizon games.
2.
Say that a finite extensive game with perfect information satisfies the
no
indifference condition
if
j
z
z
for all
j
N
whenever
i
z
z
for some
i
N
,
where
z
and
z
are terminal histories.
Show, using induction on the
length of subgames, that every player is indifferent among all subgame
perfect equilibrium outcomes of such a game.
Show also that if
s
and
s
are subgame perfect equilibria then so is
s
, where for each player
i
the
strategy
i
s
is equal to either
i
s
or
i
s
(i.e. the equilibria of the game are
interchangeable
).
3.
Two players agree to share a piece of cake using the following procedure.
First, player 1 cuts the cake into two pieces.
Then player 2 chooses one of
these two pieces for himself (so that player 1 gets the one that player 2 does
not choose).
Each player prefers more of the cake to less.
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 Winter '09
 LeungHoFung
 Computer Science, Game Theory, Tom, inﬁnitely repeated game

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