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Page 13
Figure 13.1
A convenient representation
of a twoplayer strategic game
in which each player has two actions.
Under a wide range of circumstances the preference relation
of player
i
in a strategic game can be represented
by a
payoff function
(also called a
utility function
), in the sense that
whenever
. We
refer to values of such a function as
payoffs
(or utilities). Frequently we specify a player's preference relation by
giving a payoff function that represents it. In such a case we denote the game by
rather than
.
A finite strategic game in which there are two players can be described conveniently in a table like that in Figure
13.1. One player's actions are identified with the rows and the other player's with the columns. The two numbers in
the box formed by row
r
and column
c
are the players' payoffs when the row player chooses
r
and the column
player chooses
c
, the first component being the payoff of the row player. Thus in the game in Figure 13.1 the set of
actions of the row player is {
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 Spring '10
 VINH

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