We develop an axiomatic theory of costly information acquisition . Our axioms capture the idea of constant marginal costs in information production: the cost of generating two independent signals is the sum of their costs, and the cost of generating a signal with probability half equals half the costof generating it deterministically . Together with a monotonicity and a continuity conditions, these axioms completely determine the cost of a signal up to a vector of parameters , one for each pair of states of nature . These parameters have a clear economic interpretation and determine the difficulty of distinguishing between different states. The resulting cost function, which we call log-likelihood ratio cost, is a linear combinations of the Kullback-Leibler divergences (i.e., the expected log-likelihood ratios) between the conditional signal distributions. We argue that this cost function is a versatile modeling tool , and that in various examples of information acquisition it leads to more realistic predictions than the approach based on Shannon entropy .
We develop an axiomatic theory of information acquisition that captures the idea of constant marginal costs in information production: the cost of generating two independent signals is the sum of their costs, and generating a signal with probability half costs half its original cost . Together with a monotonicity and a continuity conditions, these axioms determine the cost of a signal up to a vector of parameters . These parameters have a clear economic interpretation and determine the difficulty of distinguishing states. We argue that this cost function is a versatile modeling tool that leads to more realistic predictions than mutual information .
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costly information acquisition . Our axioms capture
information acquisition that captures
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the cost of
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equals half the costof generating it deterministically
costs half its original cost
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completely
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, one for each pair of states of nature
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between different states. The resulting cost function, which we call log-likelihood ratio cost, is a linear combinations of the Kullback-Leibler divergences (i.e., the expected log-likelihood ratios) between the conditional signal distributions.
states.
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, and that in various examples of information acquisition it
that
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the approach based on Shannon entropy
mutual information