論文

For the problem of fully allocating a social endowment of a commodity among a group of agents with single-peaked preferences, we study the consequences of manipulation for several families of rules that are not strategy-proof. Given a rule and a true preference profile, we consider the induced direct revelation game, and characterize its equilibrium allocations in terms of the profile. Our results are unequivocal: for any rule we consider, and for each true preference profile, there is a unique Nash equilibrium allocation. For the profile, it is the allocation of the uniform rule (Sprumont, 1991), the unique strategy-proof, efficient, and symmetric rule in this literature. These conclusions are drawn from two distinct sets of assumptions on the rules.

We conduct laboratory experiments for the multi-unit Vickrey auction with and without advice to subjects on strategy-proofness. The rate of truth-telling among the subjects without advice stays at 20%, whereas the rate increases to 47% among those who have received advice. By conducting similar experiments for the pay-your-bid auction, which is not strategy-proof, we confirm that the increase in truth-telling is due significantly to the net advice effect (i.e., the effect beyond the so-called experimenter demand effect). Moreover, we find that providing advice improves efficiency in the Vickrey auction, particularly in the early periods, when the subjects are less experienced. In general, subjects tend to overbid in Vickrey auction experiments. Our results indicate the possibility that providing simple advice decreases such overbidding by promoting a better understanding of the strategy-proofness of the Vickrey auction. Strategy-proof mechanisms are sometimes criticized because players often fail to recognize the benefit of telling the truth. However, our observations show that introducing advice on the property of strategy-proofness helps them behave “correctly.”

We formulate an axiomatic model to analyze the problem of probability smoothing in Naïve Bayes. We define several desirable properties of smoothing methods. Our main result shows that the Laplace smoothing method is the only one that satisfies ratio preservation, order preservation, and positivity. An alternative characterization based on reallocation-proofness is also obtained.