Characterizing implementable allocation rules in multi-dimensional environments

We study characterizations of implementable allocation rules when types are multi-dimensional, monetary transfers are allowed, and agents have quasi-linear preferences over outcomes and transfers. Every outcome is associated with a continuous valuation function that maps an agent's type to his value for this outcome. Sets of types are assumed to be convex. Our main characterization theorem implies that allocation rules are implementable if and only if they are implementable on any two-dimensional convex subset of the type set. For finite sets of outcomes, they are implementable if and only if they are implementable on every one-dimensional subset of the type set. Our results complement and extend significantly a characterization result by Saks and Yu, as well as follow-up results thereof. Contrary to our model, this stream of literature identifies types with valuation vectors. In such models, convexity of the set of valuation vectors allows for a similar characterization as ours. Furthermore, implementability on one-dimensional subsets of valuation vectors is equivalent to monotonicity. We show by example that the latter does not hold anymore in our more general setting. Our proofs demonstrate that the linear programming approach to mechanism design, pioneered in Gui et al. and Vohra, can be extended from models with linear valuation functions to arbitrary continuous valuation functions. This provides a deeper understanding of the role of monotonicity and local implementation. In particular, we provide a new, simple proof of the Saks and Yu theorem, and generalizations thereof. Modeling multi-dimensional mechanism design the way we propose it here is of relevance whenever types are given by few parameters, while the set of possible outcomes is large, and when values for outcomes are non-linear functions in types

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

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;

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

Generalized reduced-form auctions: a network-flow approach

We develop a network-flow approach for characterizing interim-allocation rules that can be implemented by ex post allocations. Our method can be used to characterize feasible interim allocations in general multi-unit auctions where agents face capacity constraints, both ceilings and floors. Applications include a variety of settings of practical interest, ranging from individual and group-specific capacity constraints, set-aside sale, partnership dissolution, and government license reallocation.Reduced-form auctions, network-flow approach, feasible circulation flow, paramodular capacity constraints

Natural implementation with partially honest agents in economic environments

In this paper, we introduce the weak and the strong notions of partially honest agents (Dutta and Sen, 2012), and then study implementation by natural price-quantity mechanisms (Saijo et al., 1996, 1999) in pure exchange economies with three or more agents in which pure-consequentialistically rational agents and partially honest agents coexist. Firstly, assuming that there exists at least one partially honest agent in either the weak notion or the strong notion, the class of efficient social choice correspondences which are Nash-implementable by such mechanisms is characterized. Secondly, the (unconstrained) Walrasian correspondence is shown to be implementable by such a mechanism when there is at least one partially honest agent of the strong type, which may provide a behavioral foundation for decentralized implementation of the Walrasian equilibrium. Finally, in this set-up, the effects of honesty on the implementation of more equitable Pareto optimal allocations can be viewed as negligible.