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.

Motivated by these considerations, we introduce the new class of contextual games .

Weaknesses: From a technical point of view, the result is an incremental enhancement of [32], and follows by connecting known results. As such, the significance of the paper relies on the originality and usefulness of the novel framework of contextual games. This is by itself of course fine, since impact and usefulness are possibly the most important aspects anyway. The main weakness of this paper is that the usefulness and motivation of the results are a bit vague. The reason is that it's not clear why would selfish players follow the proposed algorithm.

The reviewers agree that this is a good contribution to the literature on learning in games. The authors are strongly encouraged to improve presentation regarding how the various constants (e.g.

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.