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Communication rules are optimal given the decision rules if (for <math>l \in \{C,D\}\;</math>):
*<math>\mu_j(m_j|\theta_j)\;</math> is the probability of sending message <math>m_j \;</math> if the state is <math>\theta_j\;</math>
*whenever <math>\mu_j(m_j|\theta_j)>0\;</math>, <math> m_j \in arg \max_{m \in M} \mathbb{E} (\lambda \pi_j^l + (q-\lambda)\pi_k^l | theta_j )\;</math>
*where <math>\pi_j\;</math> takes <math>d_j\;</math> and <math>d_k\;</math> as given.
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