TABLE OF CONTENTS This section presents two readily identified normal form game models potential games and supermodular games which will enable us to immediately establish the following results for decision update rules:
existence and sometimes identification of an NE/steady state;
convergence conditions;
stability conditions.
As formalized by Monderer and Shapley [24], a potential game is a normal form game that has the property that there exists a function known as the potential function, V: A ? R, that reflects the change in value accrued by a unilaterally deviating player. In many ways, the concept of a potential function is identical to that of a Lyapunov function a topic discussed in section Convergence and Stability and return to in section Stability.
Given an arbitrary unilateral deviation by player j from a j to b j (the actions of the other players ( a j), remain fixed), five different types of potential games are defined by the relationship between the value accrued by the unilateral deviation, ? u i( a, b i) = u i( b i, a ?i) ? u i( a i, a ?i), and the change in value of the potential function, ? V i( a, b i) = V( b i, a ?i) ? V( a i, a ?i):
If there exists a function, V, such...
