1. Consider an agent who takes an action after receiving some in- formation. A decision problem...

 

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1. Consider an agent who takes an action after receiving some in- formation. A decision problem is a tuple (S, II, C, u, p), where S is the state space, II is the partition, C is the set of actions, u Sx C R is the utility function and p is the prior over S. Show that if partition II₁ is finer than partition II₂ then decision problem A = (S, II₁, C, u, p) is more valuable than decision problem B = (S, I1₂, C, u, p). 1. Consider an agent who takes an action after receiving some in- formation. A decision problem is a tuple (S, II, C, u, p), where S is the state space, II is the partition, C is the set of actions, u Sx C R is the utility function and p is the prior over S. Show that if partition II₁ is finer than partition II₂ then decision problem A = (S, II₁, C, u, p) is more valuable than decision problem B = (S, I1₂, C, u, p).

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In decision theory the value of a decision problem is typically assessed based on the expected utili... View the full answer