# Tag Info

Claim: If choice sets $T, M,$ and $A$ are finite, then an assessment $\{\beta^*_{r}, \beta^*_{s}, \mu^*\}$ is a WPBE (weak perfect Bayesian equilibrium) of the two-stage signalling game between receiver $r$ and sender $s$ if and only if it is a SE (sequential equilibrium). Proof: SE $\implies$ WPBE is trivial since SEs are PBEs by construction, and thus are ...
Let me answer here putting together all the hints in the comments. You've figured out that the equilibrium bid for a type $v$ bidder is $b(v) = \frac{2}{3}v$. The bids are strictly increasing in $v$, so bidder $i$ wins whenever $b(v_i) \geq b(v_j)$ or $v_i \geq v_j$. The expected payoff for a type $v$ bidder is thus $$(v -b(v))P(b_1 \geq b_2)$$ or  (...