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Alonso Dessein Matouschek (2008) - When Does Coordination Require Centralization (view source)
Revision as of 19:14, 29 September 2020
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|Has article title=When Does Coordination Require Centralization
|Has author=Alonso Dessein Matouschek
|Has year=2008
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*This page is referenced in [[PHDBA602 (Theory of the Firm)]]
==Reference(s)==
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.
Proposition 1 in the paper gives the communication equilibria: If <math>\delta \in (0, \infty)\;</math>, then for every positive interger <math>N_j\;</math>, there exists at least one equilibrium <math>(\mu_1(\cdot),\mu_2(\cdot),d_1(\cdot),d_2(\cdot),g_1(\cdot),g_2(\cdot))\;</math> where:
#<math>\mu_j(m_j|\theta_j) \sim U[a_{j,i-1},a_{j,i}]\;</math> if <math>\theta_j\;</math> in <math>(a_{j,i-1},a_{j,i})\;</math>
#<math>g_j(\theta_j|m_j) \sim U[a_{j,i-1},a_{j,i}]\;</math> if <math>\m_j\;</math> in <math>(a_{j,i-1},a_{j,i})\;</math>
#<math>a_{j,i+1}-a_{j,i} = a_{j,i} -a_{j,i-1} + 4b a_{j,i}\;</math> for <math>i=1,\ldots,N_j-1\;</math>, where <math>b = b_C\;</math> or <math>b_D\;</math> appropriately
#<math>d_j(m,\theta_j) = d_j^l\;</math>
