Analysis and Design of Cognitive Radio Networks Using Game Theory
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Potential Games

Identification Techniques(1)

This section presents various techniques by which exact and ordinal potential functions can be shown to exist and by which exact and
ordinal potential functions can be identified

there exists a simple technique for determining whether or not the game is an exact potential games

1-Twice Continuously Differentiable EPG Existence

Exact potential games forms linear space.

2-Common Exact Potential Game Forms

Many exact potential games can be recognized by the form of the utility function

Theorem(5-2-1):

Example1: Coordination-Dummy Game

Theorem(5-2-2):

Bilateral Symmetric Interaction (BSI) Games

if every player’s utility function can be characterized by:

Again, it is relatively straight-forward to demonstrate that this is an exact potential as:

BSI Games is very important in cognitive radio. for mor detail see this example:

example

Common Exact Potential Games

table(5-2):Common Exact Potential Game Forms