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# 11 game theory lecture 2 strategic form games finite

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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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