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Unformatted text preview: · · ) is an improvement path. Therefore we have,
Φ (s 0 ) < Φ (s 1 ) < · · · ,
where Φ is the ordinal potential. Since the game is ﬁnite, i.e., it has a ﬁnite
strategy space, the potential function takes on ﬁnitely many values and the above
sequence must end in ﬁnitely many steps.
This implies that in ﬁnite ordinal potential games, every “maximal”
improvement path must terminate in an equilibrium point.
That is, the simple myopic learning process based on 1sided better reply
dynamic converges to the equilibrium set.
Next week, we will show that other natural simple dynamics also converge to
a pure equilibrium for potential games.
19 Game Theory: Lecture 8 Potential Games Characterization of Finite Exact Potential Games
For a ﬁnite path γ = (s 0 , . . . , s N ), let
N I (γ) = ∑ u m (s i ) − u m (s i −1 ),
i i i =1 where mi denotes the player changing its strategy in the i th step of
the path.
The path γ = (s 0 , . . . , s N ) is closed if s 0 = s N . It is a simple closed
path if in ad...
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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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