Table 4 Information signals and their probability.

From: A game theoretic approach reveals that discretizing clinical information can reduce antibiotic misuse

Signal

Probability of appearance

Posterior probability induced by the signal

H

\(q_{\mathrm{H}} = 1 - F\left( T \right) = {\int}_T^1 {f\left( p \right){\mathrm{d}}p}\)

\(p_{\mathrm{H}} = \frac{{{\int}_T^1 {p \cdot f\left( p \right){\mathrm{d}}p} }}{{{\int}_T^1 {f\left( p \right){\mathrm{d}}p} }} = \frac{{{\int}_T^1 {p \cdot f\left( p \right){\mathrm{d}}p} }}{{1 - F\left( T \right)}}\)

L

\(q_{\mathrm{L}} = F\left( T \right) = {\int}_0^T {f\left( p \right){\mathrm{d}}p}\)

\(p_{\mathrm{L}} = \frac{{{\int}_0^T {p \cdot f\left( p \right){\mathrm{d}}p} }}{{{\int}_0^T {f\left( p \right){\mathrm{d}}p} }} = \frac{{{\int}_0^T {p \cdot f\left( p \right){\mathrm{d}}p} }}{{F\left( T \right)}}\)

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