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Unformatted text preview: rms game is a triplet �I , (Si )i ∈I , (ui )i ∈I � such that I is a ﬁnite set of players, i.e., I = {1, . . . , I }; Si is the set of available actions for player i ; si ∈ Si is an action for player i ; ui : S → R is the payoﬀ (utility) function of player i where S = ∏i Si is the set of all action proﬁles.
In addition, we use the notation s−i = [sj ]j �=i : vector of actions for all players except i . S−i = ∏j �=i Sj is the set of all action proﬁles for all players except i
(si , s−i ) ∈ S is a strategy proﬁle, or outcome.
10 Game Theory: Lecture 2 Strategic Form Games Strategies
In game theory, a strategy is a complete description of how to play
the game.
It requires full contingent planning. If instead of playing the game
yourself, you had to delegate the play to a “computer” with no
initiative, then you would have to spell out a full description of how
the game would be played in every contingency.
For example, in chess, this would be an impossible task (though in
some simpler games, it can be done).
Thinking in terms of strategies...
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This document was uploaded on 03/19/2014 for the course EECS 6.254 at MIT.
 Spring '10
 AsuOzdaglar

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