Insert \allowbreak where needed, or even better, reword the sentence - the breakpoints (after relations and binary operators) are there for a reason.
From TeX by Topic (p 207):
23.9 Line breaking in math formulas
In-line formulas can be broken after relations and binary operators. The respective penalties are the \relpenalty and the \binoppenalty. However, TeX will only break after such symbols if they are not enclosed in braces. Other breakpoints can be created with \allowbreak, which is an abbreviation for \penalty0.
Unlike in horizontal or vertical mode where putting two penalties in a row is equivalent to just placing the smallest one, in math mode a penalty placed at a break point – that is, after a relation or binary operator – will effectively replace the old penalty by the new one.
If you add \showoutput to your MWE, you can see TeX printing the insertion of the penalty after the operator = but nowhere else (the output below is for that $F_A(\pi_A) = F_A(\pi_{A},B)$ is):
....\OT1/cmr/m/n/10 t ....\OT1/cmr/m/n/10 h ....\OT1/cmr/m/n/10 a ....\OT1/cmr/m/n/10 t ....\glue 3.33333 plus 1.66666 minus 1.11111 ....\mathon ....\OML/cmm/m/it/10 F ....\hbox(4.78334+0.0)x6.51392, shifted 1.49998 .....\OML/cmm/m/it/7 A ....\OT1/cmr/m/n/10 ( ....\OML/cmm/m/it/10 ^^Y ....\hbox(4.78334+0.0)x6.51392, shifted 1.49998 .....\OML/cmm/m/it/7 A ....\OT1/cmr/m/n/10 ) ....\glue(\thickmuskip) 2.77771 plus 2.77771 ....\OT1/cmr/m/n/10 = ....\penalty 500 ....\glue(\thickmuskip) 2.77771 plus 2.77771 ....\OML/cmm/m/it/10 F ....\hbox(4.78334+0.0)x6.51392, shifted 1.49998 .....\OML/cmm/m/it/7 A ....\OT1/cmr/m/n/10 ( ....\OML/cmm/m/it/10 ^^Y ....\hbox(4.78334+0.0)x6.51392, shifted 1.49998 .....\OML/cmm/m/it/7 A ....\OML/cmm/m/it/10 ; ....\glue(\thinmuskip) 1.66663 ....\OML/cmm/m/it/10 B ....\kern0.50172 ....\OT1/cmr/m/n/10 ) ....\mathoff ....\glue 3.33333 plus 1.66666 minus 1.11111 ....\OT1/cmr/m/n/10 i ....\OT1/cmr/m/n/10 s
\allowbreakat breakable locations might help.\allowlinebreakbut it was even more obvious.