(11), p. 13 — the stage-2 subgame is a weighted potential game with potential Φ and weights v_i

In the network market with valuations $v_i>0$, benefit $f$ and potential $\Phi(B,p,q)=\sum_{i=1}^{|B|}f(i,q)-p\sum_{i\in B}1/v_i$, for every consumer $i\in N$, every set $B_{-i}\subseteq N\setminus\{i\}$ of other buyers, every price $p$ and every quality $q$,

Every unilateral deviation changes the deviator's payoff by $v_i$ times the change in $\Phi$, so the stage-2 subgame is a weighted potential game with weights $v_i$. This is what makes potential maximization available as an equilibrium-selection criterion.

Formalization Note The identity uses $v_i\neq 0$, which the standing assumptions ($v_i>0$) supply; they are taken as a hypothesis for uniformity with the other statements.