Mixable

A game {⚠ $(\Omega,\Gamma,\lambda)$} in competitive on-line prediction is {⚠ $\eta$}-mixable, where {⚠ $\eta > 0$} if there exists a substitution function for it. Or if {⚠ $\forall \gamma_1,\gamma_2 \in \Gamma, \alpha \in [0,1], \exists \delta \in \Gamma$} such as {⚠ $\forall \omega \in \Omega:$}

{⚠ $\exp(-\eta\lambda(\omega,\delta)) \ge \alpha\exp(-\eta\lambda(\omega,\gamma_1)) + (1-\alpha)\exp(-\eta\lambda(\omega,\gamma_2))$}.

In this case the loss function is also called mixable.