Peer-prediction is a mechanism which elicits privately-held, non-variable information from self-interested agents-formally, truth-telling is a strict Bayes Nash equilibrium of the mechanism. The original Peer-prediction mechanism suffers from two main limitations: (1) the mechanism must know the "common prior" of agents' signals; (2) additional undesirable and non-truthful equilibria exist which often have a greater expected payoff than the truth-telling equilibrium. A series of results has successfully weakened the known common prior assumption. However, the equilibrium multiplicity issue remains a challenge. In this paper, we address the above two problems. In the setting where a common prior exists but is not known to the mechanism we show (1) a general negative result applying to a large class of mechanisms showing truth-telling can never pay strictly more in expectation than a particular set of equilibria where agents collude to "relabel" the signals and tell the truth after relabeling signals; (2) provide a mechanism that has no information about the common prior but where truth-telling pays as much in expectation as any relabeling equilibrium and pays strictly more than any other symmetric equilibrium; (3) moreover in our mechanism, if the number of agents is sufficiently large, truth-telling pays similarly to any equilibrium close to a "relabeling" equilibrium and pays strictly more than any equilibrium that is not close to a relabeling equilibrium.
In contrast, the disagreement mechanism designed by REF is truthful and pays truth-telling strictly better than any other symmetric equilibrium if the number of agents is greater than 6.
Equilibrium Selection in Information Elicitation without Verification via Information Monotonicity
ArXiv
ArXiv
Mathematics Computer Science