  We formulate the novel class of contextual games, a type of repeated games
driven by contextual information at each round. By means of kernel-based
regularity assumptions, we model the correlation between different contexts and
game outcomes and propose a novel online (meta) algorithm that exploits such
correlations to minimize the contextual regret of individual players. We define
game-theoretic notions of contextual Coarse Correlated Equilibria (c-CCE) and
optimal contextual welfare for this new class of games and show that c-CCEs and
optimal welfare can be approached whenever players' contextual regrets vanish.
Finally, we empirically validate our results in a traffic routing experiment,
where our algorithm leads to better performance and higher welfare compared to
baselines that do not exploit the available contextual information or the
correlations present in the game.
