Nash Wardrop Equilibrium

In a population game, a configuration $x\in X$ is a Nash/Wardrop equilibrium if every strategy used with positive mass is payoff-maximizing for its population: $$ x_i(s_i)>0 \quad\text{implies}\quad K_i(s_i,x)\ge K_i(t_i,x) \quad\text{for every }t_i\in S_i. $$

The nonatomic interpretation is essential: a single agent may change strategy without changing the aggregate configuration $x$.

References

• [MFoGT, Chapter 5, Def. 5.2.2] Laraki, Renault, and Sorin, Mathematical Foundations of Game Theory. Nash/Wardrop equilibrium for population games.