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Mechanism Design with Multidimensional, Continuous Types and Interdependent Valuations. (June 2006) with Scott Johnson, John Pratt, and Richard Zeckhauser. Abstract: We consider
the mechanism design problem when agents' types are multidimensional and
continuous, and their valuations are interdependent. If there are at
least three agents whose types satisfy a weak correlation condition,
then for any decision rule there exist balanced transfers that render
truthful revelation a Bayesian ε-equilibrium. A slightly stronger
correlation condition ensures balanced transfers exist that induce a
Bayesian Nash equilibrium in which agents' strategies are nearly
truthful. Click here for the latest version of the paper.
This is an older version of the paper that has more material on the public signals case. Efficient Design with Multidimensional, Continuous Types and Interdependent Valuations Abstract: We consider mechanism design in social choice problems in which agents' types are mutually payoff-relevant, multidimensional, and take on a continuum of possible values. If the center receives a signal that is stochastically related to the agents' types and direct returns are bounded, 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 also continuous, truthful revelation becomes a nearly 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 are balanced transfers under which truthful revelation is a Bayesian epsilon-equilibrium, again for any decision rule. Analogous results hold when agents also take mutually payoff-relevant actions in advance of any action by the center. |
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