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.