We consider population games played by procedurally rational players who, when revising their current strategy, test each of available strategies independently in a series random matches –i.e., battery tests–, and then choose the strategy that performed best this tests. This revision protocol leads to so-called payoff-sampling dynamics (aka test-all Best Experienced Payoff dynamics). In paper w...

We give a new proof of theorem Lo Faro concerning minimal counterexamples to the union-closed conjecture, and we prove some results “ε-version” maximal frequency in families.

Abstract For any open hyperbolic Riemann surface $X$, the Bergman kernel $K$, logarithmic capacity $c_{\beta }$, and analytic $c_{B}$ satisfy inequality chain $\pi K \geq c^2_{\beta } c^2_B$. Moreover, equality holds at a single point between two of three quantities if only $X$ is biholomorphic to disk possibly less relatively closed polar set. We extend by showing that $c_{B}^2 \pi v^{-1}(X)$ ...