Superrational types

TL;DR

This paper provides a formal framework for superrationality in symmetric games, using epistemic game theory and coalgebra theory to analyze superrationally justifiable actions and conditions for superrational outcomes.

Contribution

It introduces a formal model of superrationality using type spaces and coalgebra theory, extending the understanding of superrational outcomes in game theory.

Findings

Conditions guaranteeing superrational outcomes identified

Formal modeling of superrationally justifiable actions established

Type spaces and coalgebra theory applied to superrationality

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.