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Alonso Dessein Matouschek (2008) - When Does Coordination Require Centralization (view source)
Revision as of 22:05, 23 November 2010
, 22:05, 23 November 2010no edit summary
Beliefs satisfy:
*<math>g(\theta_j|m) = \frac{\mu_j(m_j|\theta_j)}{\int_P \mu_j(m_j|\theta_j) d\theta_j}\;</math>
*where <math>P = \{\theta_j: \mu_j(m_j|\theta_j) >0 \}\;</math>
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>
