Superrational types

Abstract

We present a formal analysis of Douglas Hofstadter's concept of \emph{superrationality}. We start by defining superrationally justifiable actions, and study them in symmetric games. We then model the beliefs of the players, in a way that leads them to different choices than the usual assumption of rationality by restricting the range of conceivable choices. These beliefs are captured in the formal notion of \emph{type} drawn from epistemic game theory. The theory of coalgebras is used to frame type spaces and to account for the existence of some of them. We find conditions that guarantee superrational outcomes.