A game of prediction is a triple $(\Omega,\Gamma,\lambda)$, where $\Omega$ is an outcome space, $\Gamma$ is a decision space, and $\lambda:\Omega\times\Gamma\to[-\infty,\infty]$ is the loss function. Important special cases are those of:
• point predictions, where $\Gamma=\Omega$;
• probability predictions, where $\Gamma$ is the set of all probability measures on $\Omega$; if $\Omega$ is finite, the usual loss function is the log loss;
• region predictions, where $\Gamma$ is the set of all subsets of $\Omega$; the usual loss function is
$\displaystyle{ \lambda(\omega,\gamma)= \begin{cases} 1 & \text{if } \omega\in\gamma\\ 0 & \text{otherwise}.\end{cases}}$