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Analysis and Design of Cognitive Radio Networks Using Game Theory | ||
Special Properties of Potential Games
The following are some valuable properties of potential games which considers the relationship between FIP and potential games, the relationships between AFIP and potential games, the implications of equivalence properties on FIP and AFIP.
FIP and Potential Games
Theorem1 : FIP and Generalized Ordinal Potential Games All finite generalized ordinal potential games have FIP.
Theorem2:Generalized Ordinal Potential Games and FIP All games with FIP are generalized ordinal potential games.
Theorem3: Equivalence of Generalized Ordinal Potential Games and FIP , A finite normal form game has FIP if and only if it has a generalized ordinal potential.
Theorem4: FIP and AFIP, All games with FIP also have AFIP.
Theorem5:Weighted Potential Games and AFIP Every weighted potential game with a bounded potential has AFIP.
Theorem(5-3-1):
the continuity of a game’s potential function is critical to
establishing the steady-state, convergence, and stability properties for infinite potential
games. Beyond directly evaluating continuity for each potential function, it is also
possible to infer potential function continuity from utility function properties
Net Improvement Properties of Exact Potential Games
Theorem(5-3-2):
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