Unformatted text preview: ssible,
and Nash equilibrium rules out a lot of other outcomes.
Think of equilibrium selection. Equilibrium selection is hard.
Most important idea, Schelling’s focal point.
Some equilibria are more natural and will be expected.
Schelling’s example: ask the people to meet in New York, without
specifying the place. Most people will go to Grand Central. Meeting
at Grand Central, as opposed to meeting at any one of thousands of
similar places, is a “focal point”.
30 Game Theory: Lecture 2 Examples Examples: Battle of the Sexes and Matching Pennies
Example: Battle of the Sexes (players wish to coordinate but have
conﬂicting interests)
Player 1 \ Player 2 ballet football
ballet
(1, 4) (0, 0)
football
(0, 0) (4, 1)
Two Nash equilibria, (Ballet, Ballet) and (Soccer, Soccer).
Example: Matching Pennies.
Player 1 \ Player 2 heads
tails
heads
(−1, 1) (1, −1)
tails
(1, −1) (−1, 1)
No pure Nash equilibrium (but we will see in the next lecture that
there exists a unique mixed strategy equilibrium).
31 Game Theory: Lect...
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 Spring '10
 AsuOzdaglar
 Game Theory

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