An individual can only experience regret if she learns about an unchosen alternative. In many situations, learning about an unchosen alternative is possible only if someone else chose it. We develop a model where the ex-post information available to each regret averse individual depends both on their own choice and on the choices of others, as others can reveal ex-post information about what might have been. This implies that what appears to be a series of isolated single-person decision problems is in fact a rich multi-player behavioural game, the regret game, where the psychological payoffs that depend on ex-post information are interconnected. For an open set of parameters, the regret game is a coordination game with multiple equilibria, despite the fact that all individuals possess a uniquely optimal choice in isolation. We experimentally test this prediction and find support for it.