Population Game

A population game has a finite set $I$ of nonatomic populations. For each population $i$, the finite set $S_i$ lists the strategies available to agents in that population, and $$ X_i=\Delta(S_i) $$ is the simplex of population shares. A configuration is $x=(x_i)_{i\in I}\in X=\prod_i X_i$, where $x_i(s_i)$ is the proportion of population $i$ using strategy $s_i$.

The payoff data are maps $$ K_i:S_i\times X\to\mathbb R, $$ where $K_i(s_i,x)$ is the payoff of an individual agent of population $i$ who uses $s_i$ when the aggregate configuration is $x$.

References

• [MFoGT, Chapter 5, Section 5.2.1.3] Laraki, Renault, and Sorin, Mathematical Foundations of Game Theory. Population games and nonatomic strategy proportions.