  We add here another layer to the literature on nonatomic anonymous games
started with the 1973 paper by Schmeidler. More specifically, we define a new
notion of equilibrium which we call $\varepsilon$-estimated equilibrium and
prove its existence for any positive $\varepsilon$. This notion encompasses and
brings to nonatomic games recent concepts of equilibrium such as
self-confirming, peer-confirming, and Berk--Nash. This augmented scope is our
main motivation. At the same time, our approach also resolves some conceptual
problems present in Schmeidler (1973), pointed out by Shapley. In that paper\
the existence of pure-strategy Nash equilibria has been proved for any
nonatomic game with a continuum of players, endowed with an atomless countably
additive probability. But, requiring Borel measurability of strategy profiles
may impose some limitation on players' choices and introduce an exogenous
dependence among\ players' actions, which clashes with the nature of
noncooperative game theory. Our suggested solution is to consider every subset
of players as measurable. This leads to a nontrivial purely finitely additive
component which might prevent the existence of equilibria and requires a novel
mathematical approach to prove the existence of $\varepsilon$-equilibria.
