In various occasions an agent may hold preferences on others that depend on the preferences those others report; for example, a university will naturally prefer to hire a researcher who values working for it. We focus on one-to-one matching problems of social choice theory, where each element of a set has a preference ranking over the elements of another set of equal size, and pairs must be formed between the two sets. Applying the Deferred-Acceptance matching solution, with researchers as proposers and universities as receivers, we introduce a reciprocity function reflecting universities' preferences based on researchers' rankings. Unlike the classical setting, this can incentivise researchers to strategically misreport their sincere preferences in order to obtain a better pair. Moreover, if they do so in iteration the process may never terminate. We study the convergence of such processes under different reciprocity criteria, which we formalise as axioms.
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