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Handbook of Game Theory by Shmuel Zamir, Petyon Young

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13.6 Potential Games

In this section and the following two, we consider classes of population games that have attractive theoretical properties and are useful in applications. Games in these classes admit simple characterizations of Nash equilibrium, and ensure global convergence under various evolutionary dynamics.

The most general convergence results are available for potential games, in which all information about incentives can be captured by a scalar-valued function defined on the set of population states. Dynamics satisfying positive correlation (PC) and Nash stationarity (NS) ascend this function and converge to Nash equilibrium.

The first appearance of potential functions in game theory is in the work of Beckmann et al. (1956), who ...

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