Sketch of Solutions to Problem Set 1
Ying Chen,
ECN 416 Game Theory
1.
Consider the following game:
2
1
3
1
1
0
2
1
3
1
2
2
1
0
0
1
1
2
3
0
(a)
Assume that both players are rational. What happens?
If player
1
is rational, he won’t play
since
is strictly dominated by
.
If player
2
is rational, he won’t play
since
is strictly dominated by
.
(b)
Assume that both players are rational and that each believes that the other is
rational. What happens?
Player
1
won’t play
since it is now strictly dominated by
.
Player
2
won’t play
since it is now strictly dominated by
.
(c)
Find the strategies that survive the iterated deletion of strictly dominated strate
gies.
(
)
2. Iterated Deletion of (weakly) Dominated Strategies
Consider the following
twoplayer game
2
1
1
0
1
3
1
1
1
0
2
2
1
3
1
3
3
1
2
2
(a)
Are there any strictly dominated strategies? Are there any weakly dominated
strategies? If so, explain what dominates what and how.
No strictly dominated strategies.
Weakly dominated strategies:
weakly dominates
;
weakly dominates
.
(b)
After deleting any strictly or weakly dominated strategies, are there any strictly
or weakly dominated strategies in the ‘reduced’ game? If so, explain what dominates
what and how. What is left?
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After deleting
and
,
weakly dominates
and
weakly dominates
. What’s
left is
(
)
.
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 Spring '10
 Y.Chen
 Game Theory, player, strictly dominated strategies, weakly dominated strategies, Ying Chen

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