Undominated Groves Mechanisms

The family of Groves mechanisms, which includes the well-known VCG mechanism (also known as the Clarke mechanism), is a family of efficient and strategy-proof mechanisms. Unfortunately, the Groves mechanisms are generally not budget balanced. That is, under such mechanisms, payments may flow into or out of the system of the agents, resulting in deficits or reduced utilities for the agents. We consider the following problem: within the family of Groves mechanisms, we want to identify mechanisms that give the agents the highest utilities, under the constraint that these mechanisms must never incur deficits. We adopt a prior-free approach. We introduce two general measures for comparing mechanisms in prior-free settings. We say that a non-deficit Groves mechanism $M$ {\em individually dominates} another non-deficit Groves mechanism $M'$ if for every type profile, every agent's utility under $M$ is no less than that under $M'$, and this holds with strict inequality for at least one type profile and one agent. We say that a non-deficit Groves mechanism $M$ {\em collectively dominates} another non-deficit Groves mechanism $M'$ if for every type profile, the agents' total utility under $M$ is no less than that under $M'$, and this holds with strict inequality for at least one type profile. The above definitions induce two partial orders on non-deficit Groves mechanisms. We study the maximal elements corresponding to these two partial orders, which we call the {\em individually undominated} mechanisms and the {\em collectively undominated} mechanisms, respectively.Comment: 34 pages. To appear in Journal of AI Research (JAIR

Undominated Groves Mechanisms

The family of Groves mechanisms, which includes the well-known VCG mechanism (also known as the Clarke mechanism), is a family of efficient and strategy-proof mechanisms. Unfortunately, the Groves mechanisms are generally not budget balanced. That is, under such mechanisms, payments may flow into or out of the system of the agents, resulting in deficits or reduced utilities for the agents. We consider the following problem: within the family of Groves mechanisms, we want to identify mechanisms that give the agents the highest utilities, under the constraint that these mechanisms must never incur deficits. We adopt a prior-free approach. We introduce two general measures for comparing mechanisms in prior-free settings. We say that a non-deficit Groves mechanism M in- dividually dominates another non-deficit Groves mechanism M′ if for every type profile, every agent’s utility under M is no less than that under M′, and this holds with strict inequality for at least one type profile and one agent. We say that a non-deficit Groves mechanism M collectively dominates another non-deficit Groves mechanism M′ if for every type profile, the agents’ total utility under M is no less than that under M′, and this holds with strict inequality for at least one type profile. The above definitions induce two partial orders on non-deficit Groves mechanisms. We study the maximal elements corresponding to these two partial orders, which we call the individually undominated mechanisms and the collectively undominated mechanisms, respectively

Large Market Design in Dominance

This paper introduces a new concept of market mechanism design into general economic environments with finite but many traders, where multiple objects are traded and any combination of complements and substitutes is permitted. The auctioneer randomly divides traders into multiple groups. Within each group, trades occur at the market-clearing price vector of another group. With private values, any undominated strategy profile mimics price-taking behavior, enforcing perfect competition. With interdependent values, any twice iteratively undominated strategy profile mimics the rational expectations equilibrium, enforcing ex post efficiency. Our mechanisms are detail-free, i.e., they do not depend on the details of model specification.

"Large Market Design in Dominance"

This paper introduces a new concept of market mechanism design into general economic environments with finite but many traders, where multiple objects are traded and any combination of complements and substitutes is permitted. The auctioneer randomly divides traders into multiple groups. Within each group, trades occur at the market-clearing price vector of another group. With private values, any undominated strategy profile mimics price-taking behavior, enforcing perfect competition. With interdependent values, any twice iteratively undominated strategy profile mimics the rational expectations equilibrium, enforcing ex post efficiency. Our mechanisms are detail-free, i.e., they do not depend on the details of model specification.

"On Detail-Free Mechanism Design and Rationality"

The study of mechanism design is sometimes criticized, because the designed mechanisms depend on the fine detail of the model specification, and agents' behavior relies on the strong common knowledge assumptions on their rationality and others. Hence, the study of 'detail-free' mechanism design with weak informational assumptions is the most important to make as the first step towards a practically useful theory. This paper will emphasize that even if we confine our attentions to detail-free mechanisms with week rationality, there still exist a plenty of scope for development of new ideas on how to design a mechanism to play the powerful role. We briefly explain my recent works on this line, and argue that the use of stochastic decision works much in large exchange economics, and agents' moral preferences can drastically improve implementability of social choice functions.

Secure implementation

Strategy-proofness, requiring that truth-telling be a dominant strategy, is a standard concept in social choice theory. However, this concept has serious drawbacks. In particular, many strategy-proof mechanisms have multiple Nash equilibria, some of which produce the wrong outcome. A possible solution to this problem is to require double implementation in Nash equilibrium and in dominant strategies, i.e., secure implementation. We characterize securely implementable social choice functions and investigate the connections with dominant strategy implementation and robust implementation. We show that in standard quasi-linear environments with divisible private or public goods, there exist surplus-maximizing (non-dictatorial) social choice functions that can be securely implemented.Nash implementation, robust implementation, secure implementation, strategy-proofness

On Detail-Free Mechanism Design and Rationality

The study of mechanism design is sometimes criticized, because the designed mechanisms depend on the fine detail of the model specification, and agents' behavior relies on the strong common knowledge assumptions on their rationality and others. Hence, the study of 'detail-free' mechanism design with weak informational assumptions is the most important to make as the first step towards a practically useful theory. This paper will emphasize that even if we confine our attentions to detail-free mechanisms with week rationality, there still exist a plenty of scope for development of new ideas on how to design a mechanism to play the powerful role. We briefly explain my recent works on this line, and argue that the use of stochastic decision works much in large exchange economics, and agents' moral preferences can drastically improve implementability of social choice functions.