Characterization of revenue equivalence

The property of an allocation rule to be implementable in dominant strategies by a unique payment scheme is called \emph{revenue equivalence}. In this paper we give a characterization of revenue equivalence based on a graph theoretic interpretation of the incentive compatibility constraints. The characterization holds for any (possibly infinite) outcome space and many of the known results are immediate consequences. Moreover, revenue equivalence can be identified in cases where existing theorems are silent

Optimal Mechanisms for Single Machine Scheduling

We study the design of optimal mechanisms in a setting where job-agents compete for being processed by a service provider that can handle one job at a time. Each job has a processing time and incurs a waiting cost. Jobs need to be compensated for waiting. We consider two models, one where only the waiting costs of jobs are private information (1-d), and another where both waiting costs and processing times are private (2-d). Probability distributions represent the public common belief about private information. We consider discrete and continuous distributions. In this setting, an optimal mechanism minimizes the total expected expenses to compensate all jobs, while it has to be Bayes-Nash incentive compatible. We derive closed formulae for the optimal mechanism in the 1-d case and show that it is efficient for symmetric jobs. For non-symmetric jobs, we show that efficient mechanisms perform arbitrarily bad. For the 2-d discrete case, we prove that the optimal mechanism in general does not even satisfy IIA, the `independent of irrelevant alternatives'' condition. Hence any attempt along the lines of the classical auction setting is doomed to fail. In the 2-d discrete case, we also show that the optimal mechanism is not even efficient for symmetric agents.operations research and management science;

Characterization of Revenue Equivalence

The property of an allocation rule to be implementable in dominant strategies by a unique payment scheme is called revenue equivalence. In this paper we give a characterization of revenue equivalence based on a graph theoretic interpretation of the incentive compatibility constraints. The characterization holds for any (possibly infinite) outcome space and many of the known results are immediate consequences. Moreover, revenue equivalence can be identified in cases where existing theorems are silent.computer science applications;

Continuous Implementation

It is well-known that mechanism design literature makes many simplifying infor- mational assumptions in particular in terms of common knowledge of the environment among players. In this paper, we introduce a notion of continuous implementation and characterize when a social choice function is continuously implementable. More specif- ically, we say that a social choice function is continuously (partially) implementable if it is (partially) implementable for types in the model under study and it continues to be (partially) implementable for types "close" to this initial model. We ?rst show that if the model is of complete information a social choice function is continuously (partially) implementable only if it satis?es Maskin?s monotonicity. We then extend this result to general incomplete information settings and show that a social choice function is continuously (partially) implementable only if it is fully implementable in iterative dominance. For ?nite mechanisms, this condition is also su¢ cient. We also discuss implications of this characterization for the virtual implementation approach.High order beliefs, robust implementation

A Characterization of Virtual Bayesian Implementation

We provide a characterization of virtual Bayesian implementation in pure strategies for environments satisfying no-total-indifference. A social choice function in such environments is virtually Bayesian implementable if and only if it satisfies incentive compatibility and a condition we term virtual monotonicity. The latter is weaker than Bayesian monotonicity - known to be necessary for Bayesian implementation. Virtual monotonicity is weak in the sense that it is generically satisfied in environments with at least three alternatives. This implies that in most environments virtual Bayesian implementation is as successful as it can be (incentive compatibility is the only condition needed).Virtual monotonicity, Bayesian monotonicity, Maskin monotonicity, virtual Bayesian implementation, incentive compatibility, type diversity, decentralization, incomplete information

On the legitimacy of coercion for the nancing of public goods

The literature on public goods has shown that e?cient outcomes are impossible if participation constraints have to be respected. This paper addresses the question whether they should be imposed. It asks under what conditions e?ciency considerations justify that individuals are forced to pay for public goods that they do not value. It is shown that participation constraints are desirable if public goods are provided by a malevolent Leviathan. By contrast, with a Pigouvian planner, e?ciency can be achieved. Finally, the paper studies the delegation of public goods provision to a pro?t-maximizing ?rm. This also makes participation constraints desirable

Characterization of Revenue Equivalence

The property of an allocation rule to be implementable in dominant strategies by a unique payment scheme is called revenue equivalence. In this paper we give a characterization of revenue equivalence based on a graph theoretic interpretation of the incentive compatibility constraints. The characterization holds for any (possibly in¯nite) outcome space and many of the known results about revenue equivalence are immediate consequence

Ordinally Bayesian incentive-compatible voting schemes

We study strategic voting after weakening the notion of strategy-proofness to Ordinal Bayesian Incentive Compatibility (OBIC). Under OBIC, truthelling is required to maximize the expected utility being computed with respect to the voter's prior beliefs and under the assumption that everybody else is also telling the truth. We show that for a special type of priors i.e., the uniform priors there exists a large class of social choice functions that are OBIC. However, for priors which are generic in the set of independent beliefs a social choice function is OBIC only if it is dictatorial. This result underlines the robustness of the Gibbard-Satterthwaite Theorem.