Potential in Population Games

A novel notion of potential in population games is presented. A population game is defined, very broadly, as any bivariant function g(x,y) on a convex set in a linear topological space. This function may specify the payoff to an individual population member from choosing strategy x (in a symmetric population game) or the mean payoff to individuals from playing according to strategy profile x (in an asymmetric game), with the choices in the population as a whole expressed by the population strategy y. These notions of population game and potential include a number of earlier notions as special cases. Potential is closely linked with (a general notion of) equilibrium. It increases along every improvement curve: the population-game analog of an improvement path in an N-player game.