Incomplete information, self-confidence, and positive sorting

This paper proposes a novel model of decentralized matching process without transfer. In my model, I adopt the behavioral assumption based on the novel interpretation of an iterative version of the Gale–Shapley algorithm. Specifically, each myopic proposer is initially optimistic about a reviewer’s acceptance rate, to the extent that they pay no attention to it; however, after experiencing a prematching failure, they become sufficiently underconfident to prioritize it when deciding on whom to apply. By incorporating this behavioral assumption into a standard dynamic game process where a strategic proposer updates his assessment of the acceptance rate of each reviewer after each trial based on the information about rivals’ actions in the trial, the model rationalizes both positive sorting and proposer-optimal stable matching as a limit point of the process. I show that the relative occurrence of each type of matching depends only on the information environment of proposers.