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A standing question in the theory of matching markets is how to define stability under incomplete information. The crucial obstacle is that a notion of stability must include a theory of how beliefs are updated in a blocking pair. This paper proposes a novel non-cooperative and epistemic approach. Agents negotiate through offers. Offers are interpreted according to the highest possible degree of rationality that can be ascribed to their proponents, in line with the principle of forward-induction reasoning.  This approach leads to a new definition of stability. The main result shows an equivalence between this notion and "incomplete-information stability", a cooperative solution concept recently put forward by Liu, Mailath, Postlewaite and Samuelson (2014), for a class of markets with one-sided incomplete information.  The result implies that forward-induction reasoning leads to efficient matchings under standard supermodularity conditions. In addition, it provides an epistemic foundation for incomplete-information stability. The paper also shows new connections and distinctions between the cooperative and the non-cooperative approach in matching markets.

The paper can be found at:  http://www.kellogg.northwestern.edu/faculty/pomatto/Stability.pdf