Two agents have to choose one of three alternatives. Their ordinal rankings of these alternatives are commonly known among them. The rankings are diametrically opposed to each other. Ex-ante efficiency requires that they reach a compromise, that is choose the alternative which they both rank sec- ond, if and only if the sum of their von Neumann Morgenstern utilities from this alternative exceeds the sum of utilities when either agent's favorite al- ternative is chosen. We assume that the von Neumann Morgenstern utilities of the middle ranked alternative are independent and identically distributed, privately observed random variables, and ask whether there are incentive compatible decision rules which elicit utilities and implement efficient deci- sions. We show that no such decision rules exist if the distribution of agents' types has a density with full support. We also study the problem of finding second-best decision rules in our set-up, and explain how this problem differs from more familiar second best problems. Finally, we give some numerical insights into the nature of second-best rules. For a variety of distributions of types, second-best rules involve very little inefficiency.
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Paper provided by Department of Economics, University of Birmingham in its series Discussion Papers with number
06-11.
Find related papers by JEL classification: C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
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