Table 1 Model terms
\(P\) | Security valuation for the representative agent |
\(t\) | Time period |
\(I_{n}\) | News shock conveying an unambiguous security value at time \(n\) |
\(n \in \left\{ {0, \ldots ,M} \right\}\) | Period, \(t = n\), when news shock \(I_{n}\) occurred |
\(j \in \left\{ {0, \ldots ,M\left| j \right\rangle n} \right\}\) | Period, \(t = j\), when news shock \(I_{{j > n}}\) occurred |
\(\theta _{n} \in \left[ {0,1} \right]\) | Weighted share of news shock \(I_{n}\);\(~\mathop \sum \limits_{{n = 0}}^{M} \theta _{n} = 1\) |
\(S_{n} \ge 0\) | Information weight of news shock \(I_{n}\) |
\(\omega _{n} \in \left\{ {0,1} \right\}\) | Real or fake news indicator for \(I_{n}\); information credibility |
\(\rho \in \left[ {0.5,1} \right]\) | Ability to distinguish between real and fake news |
\(\rho _{0} \in \left[ {0.5,1} \right]\) | Initial ability to distinguish between real and fake news |
\(\delta \in \left[ {0,1} \right]\) | Irrelevance multiplier of old news shocks |
\(\varphi \in \left[ {0,1} \right]\) | Time decay factor of spurious information |
\(\alpha \ge 1\) | Virality factor of fake news |
\(\gamma \in \left\{ {0,1} \right\}\) | Signalled presence of fake news indicator |
\(\mu \in \left[ {0,1} \right]\) | Fake news uncertainty factor |