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Nash equilibrium, dominant strategies, and dominant strategy equilibrium
The table below shows a normal (or strategic) form game with two players, Raoul and
Cal. Raoul has two strategies, Up and Down; Cal’s two strategies are West and East.
Cal
West
East
Up
a, b
e, f
Raoul
Down
c, d
g, h
The ordered pairs in the cells of the table represent the payoffs to each player resulting
from the various combinations of strategies. The first letter in each pair represents
Raoul’s payoff, the second, Cal’s. Thus, for example, if Raoul plays Down and Cal plays
West, Raoul’s payoff is
c
and Cal’s is
d
.
A
Nash equilibrium
is a strategy pair with the property that neither player can gain by
changing strategy. Each player’s strategy is a
best response
to the strategy played in the
Nash equilibrium by the other player. A Nash equilibrium strategy pair is
stable
and
self
enforcing
in that each player has no incentive to change his or her actions given what the
other player is doing.
Thus, for example, the strategy pair (Up, West) is a Nash equilibrium if and only if
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 Spring '08
 Staff

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