We consider mechanism design in social choice problems in which agents’ types are continuous, multidimensional, and mutually payoff-relevant, and there are three or more agents. If the center receives a signal that is stochastically related to the agents’ types and direct returns are bounded, then for any decision rule there is a balanced transfer function that ensures that any strategy that is not arbitrarily close to truthful is dominated by one that is. If direct returns are continuous as well, truthful revelation becomes an -dominant strategy, all Bayes-Nash equilibrium strategies are nearly truthful, and at least one such strategy exists. If the center’s information is not informative but agents’ types are stochastically related, then there exist balanced transfers under which truthful revelation is a Bayesian -equilibrium, again for any decision rule. Analogous results hold for decentralized decision problems when agents also take mutually payoff-relevant actions in advance of any action by the center.
Johnson, Scott, Nolan Miller, John W. Pratt, and Richard Zeckhauser. "Efficient Design with Multidimensional, Continuous Types, and Interdependent Valuations." KSG Faculty Research Working Papers Series RWP03-020, March 2003.