Borgers, T; Postl, P; (2004) Efficient compromising. (Discussion Papers in Economics 04-08). Department of Economics, University College London, UCL (University College London), Department of Economics, University College: London, UK.

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Abstract

Two agents have to choose one of three alternatives. Their ordinal rankingsof these alternatives are commonly known among them. The rankings are diametricallyopposed to each other. Ex-ante efficiency requires that they reacha compromise, that is choose the alternative which they both rank second,if and only if the sum of their von Neumann Morgenstern u tilities from thisalternative exceeds the sum of utilities when either agent's most preferred alternative is chosen. We assume that the von Neumann Morgenstern utilitiesof the middle ranked alternative are independent and identically distributed,privately observed random variables, and ask whether there are incentivecompatible decision rules which elicit utilities and implement efficient decisions.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 findingsecond-best decision rules in our set-up , and explain how this problem differsfrom more familiar second-best problems. Finally, we give some numericalinsights into the nature of second-best rules. For a variety of distributions oftypes, second-best rules involv every little inefficiency. Two agents have to choose one of three alternatives. Their ordinal rankingsof these alternatives are commonly known among them. The rankings are diametricallyopposed to each other. Ex-ante efficiency requires that they reacha compromise, that is choose the alternative which they both rank second,if and only if the sum of their von Neumann Morgenstern u tilities from thisalternative exceeds the sum of utilities when either agent's most preferred alternative is chosen. We assume that the von Neumann Morgenstern utilitiesof the middle ranked alternative are independent and identically distributed,privately observed random variables, and ask whether there are incentivecompatible decision rules which elicit utilities and implement efficient decisions.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 findingsecond-best decision rules in our set-up , and explain how this problem differsfrom more familiar second-best problems. Finally, we give some numericalinsights into the nature of second-best rules. For a variety of distributions oftypes, second-best rules involv every little inefficiency.

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