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Ordinal Bayesian Incentive Compatibility of Truth-telling in Stable Mechanisms in Monotonic Matching Markets

Jordi Masso (Universitat Autonoma de Barcelona)

18 mai 2017  -  11:00-12:30, salle Extranef 109

Host(s): Bettina Klaus

We study strategic behavior of agents participating in centralized stable mechanisms in two-sided many-to-one matching markets when each agent has incomplete information about the preferences of the other agents. It is known that in any stable mechanism there is a strong link between ordinal Bayesian Nash equilibria under incomplete information and Nash equilibria under complete information: given a common belief, a strategy is an ordinal Bayesian Nash equilibrium in a stable mechanism if and only if at each profile in the support of the belief the strategy prescribes a Nash equilibrium in the stable mechanism under complete information at the profile. In this paper we show that in the workers-optimal stable mechanism this link does not hold for truth-telling if firms' preferences over families of subsets of workers are monotonic responsive extensions of their rankings over individual workers. Firms have monotonic responsive extensions if having all positions filled with acceptable workers is always strictly preferred to having some positions vacant. However, we show that in the firms-optimal stable mechanism the link holds for truth-telling: given a common belief, truth-telling is a monotonic ordinal Bayesian Nash equilibrium in the firms' optimal stable mechanism under incomplete information if and only if truth-telling is a monotonic Nash equilibrium under complete information at each profile in the support of the common belief.

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