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Unformatted text preview: a = 1), then
U (a ) = ∑ pia u (ci ) .
i 6 Game Theory: Lecture 2 Introduction DecisionMaking under Uncertainty (continued)
Given expected utility theory and our postulate of “rationality,” single
person decision problems are (at least conceptually) simple.
If there are two actions, a and b , inducing probability distributions
F a (c ) and F b (c ), then the individual chooses a over b only if
U (a ) = � u (c ) dF a (c ) ≥ U (b ) = � u (c ) dF b (c ) . 7 Game Theory: Lecture 2 Introduction From Single Person to Multiperson Decision Problems
But in a multiagent situation, the utility of an agent or probability
distribution over outcomes depends on actions of others.
A simple game of “partnership” represented as a matrix game:
Player 1 \ Player 2 work hard shirk
work hard
(−1, 1)
(2, 2)
shirk
(1, −1)
(0, 0)
Here the ﬁrst number is the payoﬀ to player (partner) 1 and the
second number is the payoﬀ to player 2. More formally, the cell
indexed by row x and column y cont...
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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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