3. Consider a state space S {$1, S2, S3, S4, S5}. There are two agents, i...

 

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3. Consider a state space S {$1, S2, S3, S4, S5}. There are two agents, i = 1,2, with a common prior p = (0.3, 0.1,0.2, 0.3, 0.1). Agent 1 has information partition II₁ = {{$₁, $2}, {$3}, {$4, $5}} and 2 has information partition II2 = {{$3, $2}, {$4}, {81, 85}}. = (a) Given common prior p and information structures II₁, I2, derive types t₁(s), t₂(s), for each s € S. (b) Given the types t₁ and to that you have derived in the previous question, find probability distribution p₁ € AS that is a prior for agent 1 and P2 EAS that is a prior for agent 2, where P1, P2P. Is there a common prior, different from P, that assigns positive probability to all states? (c) Suppose that 1's prior is p₁ = (0.2, 0.1, 0.3, 0.2,0.2) and 2's prior is p2 (0.3, 0.1, 0.2, 0.2, 0.2). Find an ex ante bet and an interim bet. = 3. Consider a state space S {$1, S2, S3, S4, S5}. There are two agents, i = 1,2, with a common prior p = (0.3, 0.1,0.2, 0.3, 0.1). Agent 1 has information partition II₁ = {{$₁, $2}, {$3}, {$4, $5}} and 2 has information partition II2 = {{$3, $2}, {$4}, {81, 85}}. = (a) Given common prior p and information structures II₁, I2, derive types t₁(s), t₂(s), for each s € S. (b) Given the types t₁ and to that you have derived in the previous question, find probability distribution p₁ € AS that is a prior for agent 1 and P2 EAS that is a prior for agent 2, where P1, P2P. Is there a common prior, different from P, that assigns positive probability to all states? (c) Suppose that 1's prior is p₁ = (0.2, 0.1, 0.3, 0.2,0.2) and 2's prior is p2 (0.3, 0.1, 0.2, 0.2, 0.2). Find an ex ante bet and an interim bet. =

Answer rating: 100% (QA)

a To derive the types of each agent we need to use the information structures of each agent The type ... View the full answer