Ungrounded Payoffs: A Tale of Perfect Love and Hate

Abstract

I explore a game-theoretic analysis of social interactions in which each agent’s well-being depends crucially on the well-being of another agent. As a result of this, payoffs are interdependent and cannot be fixed, and hence the overall assessment of strategies becomes ungrounded. A paradigmatic example of this general phenomenon occurs when both players are ‘reflective altruists’, in a sense to be explained. I argue that ungroundedness cannot be captured by standard games with incomplete information, but that it requires the concept of an underspecified game; underspecified games have radically underdetermined matrices. Players locked in ungroundedness will be assumed to engage simultaneously in an implicit second-order game in which they try to coordinate their first-order matrices. If they fail to coordinate, their first-order interaction cannot be recast as a game in the first place.