Unformatted text preview: is important.
But in strategic form games, there is no diﬀerence between an action
and a pure strategy, and we will use them interchangeably. 11 Game Theory: Lecture 2 Strategic Form Games Finite Strategy Spaces
When the Si is ﬁnite for all i , we call the game a ﬁnite game.
For 2 players and small number of actions, a game can be represented
in matrix form.
Recall that the cell indexed by row x and column y contains a pair,
(a, b ) where a = u1 (x , y ) and b = u2 (x , y ).
Example: Matching Pennies.
Player 1 \ Player 2 heads
tails
heads
(−1, 1) (1, −1)
tails
(1, −1) (−1, 1)
This game represents pure conﬂict in the sense that one player’s
utility is the negative of the utility of the other player. Thus zero
sum game.
More generally true for strictly competitive games, that is, games in
which whenever one player wins the other one loses, though the sum of
the payoﬀs need not be equal to 0.
12 Game Theory: Lecture 2 Strategic Form Games Inﬁnite Strategy Spaces
Example: Cournot competition.
Two ﬁrms producing a homogeneous good for the same market.
The action of a player i is a quantity, si ∈ [0, ∞] (amount of good he
produces).
The utility for each player is its total revenue...
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 Spring '10
 AsuOzdaglar
 Game Theory

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