<Para ID="Par1">We introduce a “nestedness” relation for a general class of sender–receiver games and compare equilibrium properties, in particular the amount of information transmitted, across games that are nested. Roughly, game <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$B$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>B</mi> </math> </EquationSource> </InlineEquation> is nested in game <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$A$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>A</mi> </math> </EquationSource> </InlineEquation> if the players’ optimal...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></para>