Potential in population games

Abstract A general, novel notion of potential in population games is presented. A population game is defined, very broadly, as any bivariate function $$g\left( {x,y} \right)$$ g x , y on a convex set in a linear topological space. This function may specify the payoff for an individual population member from choosing strategy $$x$$ x (in a symmetric population game) or the mean payoff to individuals from playing according to strategy profile $$x$$ x (in an asymmetric population game), with the choices in the population as a whole expressed by the population strategy $$y$$ 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 $$N$$ N -player game.