**Santiago Guisasola 1,\* and Donald Saari 2,3,4**


Received: 27 June 2020; Accepted: 6 August 2020; Published: 17 August 2020

**Abstract:** Lower one- or two-dimensional coordination, or potential games, are popularly used to model interactive behavior, such as innovation diffusion and cultural evolution. Typically, this involves determining the "better" of competing solutions. However, examples have demonstrated that different measures of a "good" choice can lead to conflicting conclusions; a fact that reflects the history of game theory in equilibrium selection. This behavior is totally explained while extending the analysis to the full seven-dimensional class of potential games, which includes coordination games.

**Keywords:** potential games; social welfare; risk dominance; payoff dominance; innovation diffusion; externalities; decomposition
