§3.2, p. 12, (6)–(7) — informative equilibrium iff both incentive conditions hold

In the two-type A-Learning game under its standing assumptions, an informative separating equilibrium exists if and only if both buyer types prefer truthful communication to imitating the other type:

Here $u(\theta,\hat\theta)$ is the buyer's expected payoff when its actual type is $\theta$, the seller believes $\hat\theta$, and the seller designs at its optimum for that belief.

The equivalence connects the full cheap-talk equilibrium conditions to the two explicit incentive constraints (6) and (7).

Formalization Note An equilibrium includes a separating message rule, on-path belief consistency, attained seller optimality over nonnegative quality, and buyer optimality against every message. The pricing stage is represented by equation (5).