Stable matching under forward-induction reasoning

A standing question in the theory of matching markets is how to define stability under incomplete information. This paper proposes an epistemic approach. Agents negotiate through offers, and offers are interpreted according to the highest possible degree of rationality that can be ascribed to their proponents. A matching is deemed ``stable'' if maintaining the current allocation is a rationalizable action for each agent. The main result shows an equivalence between this notion and ``incomplete-information stability,'' a cooperative solution concept put forward by Liu, Mailath, Postlewaite and Samuelson (2014) for markets with incomplete information.