Utilities

Each agent gets a utility $U_i(d) = P_r - C_r$ when consuming a document it likes, otherwise its $-C_r$.
When two agents meet each must decide whether to tell the other about a document it likes:

Nothing Send

Nothing 0,0 $x_i(j), -C_m$

Send $-C_m, x_j(i)$ $x_i(j)-C_m, x_j(i)-C_m$

where \[ x_i(j) = r_i(j) (Pr[L_i(d)\,|\,L_j(d)] \cdot(P_r - C_r) + (1 - Pr[L_i(d)\,|\,L_j(d)])\cdot(-C_r)) \]
If we assume that $i$ knows which documents $j$ has read then we can approximate it using observations: \[ x_i(j) \approx \frac{|L_i^i \cap L_i^j|}{|L_i^j|}\cdot(P_r - C_r) + \left(1 - \frac{|L_i^i \cap L_i^j|}{|L_i^j|}\right)\cdot(- C_r). \]