The limits of ex post implementation

The sensitivity of Bayesian implementation to agents' beliefs about others suggests the use of more robust notions of implementation such as ex-post implementation, which requires that each agent' s strategy be optimal for every possible realization of the types of other agents. We show that the only deterministic social choice functions that are ex-post implementable in generic mechanism design frameworks with multi-dimensional signals, interdependent valuations and transferable utilities, are constant functions. In other words, deterministic ex-post implementation requires that the same alternative must be chosen irrespective of agents' signals. The proof shows that ex-post implementability of a non-trivial deterministic social choice function implies that certain rates of information substitution coincide for all agents. This condition amounts to a system of differential equations that are not satis�ed by generic valuation functions

"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.

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.

Robust Mechanism Design: An Introduction

This essay is the introduction for a collection of papers by the two of us on "Robust Mechanism Design" to be published by World Scientific Publishing. The appendix of this essay lists the chapters of the book. The objective of this introductory essay is to provide the reader with an overview of the research agenda pursued in the collected papers. The introduction selectively presents the main results of the papers, and attempts to illustrate many of them in terms of a common and canonical example, the single unit auction with interdependent values. In addition, we include an extended discussion about the role of alternative assumptions about type spaces in our work and the literature, in order to explain the common logic of the informational robustness approach that unifies the work in this volume.Mechanism design, Robust mechanism design, Common knowledge, Universal type space, Interim equilibrium, Ex post equilibrium, Dominant strategies, Rationalizability, Partial implementation, Full implementation, Robust implementation

Ex Post Implementation

We analyze the problem of fully implementing a social choice set in ex post equilibrium. Weidentify an ex post monotonicity condition that is necessary and -- in economic environments -- sufficient for full implementation in ex post equilibrium. We also identify an ex post monotonicityno veto condition that is sufficient. Ex post monotonicity is satisfied in all single crossing environments with strict ex post incentive constraints. In many economically significant environments, ex post implementation can be achieved in the direct mechanism. We show by means of two classic examples that ex post monotonicity does not imply nor is it implied by Maskin monotonicity (necessary and almost sufficient for complete information implementation). The single unit auction with interdependent valuations is shown to satisfy ex post monotonicity but not Maskin monotonicity. Ex post implementation in the direct mechanism is also possible in this case. We describe an example where the Pareto correspondence fails ex post monotonicity but Maskin monotonicity is satisfied.Ex post equilibrium, Implementation, Single crossing, Interdependent values

The Theory of Implementation of Social Choice Rules

Suppose that the goals of a society can be summarized in a social choice rule, i.e., a mapping from relevant underlying parameters to final outcomes. Typically, the underlying parameters (e.g., individual preferences) are private information to the agents in society. The implementation problem is then formulated: under what circumstances can one design a mechanism so that the private information is truthfully elicited and the social optimum ends up being implemented? In designing such a mechanism, appropriate incentives will have to be given to the agents so that they do not wish to misrepresent their information. The theory of implementation or mechanism design formalizes this “social engineering” problem and provides answers to the question just posed. I survey the theory of implementation in this article, emphasizing the results based on two behavioral assumptions for the agents (dominant strategies and Nash equilibrium). Examples discussed include voting, and the allocation of private and public goods under complete and incomplete information.Implementation Theory, Mechanism Design, Asymmetric Information, Decentralization, Game Theory, Dominance, Nash Equilibrium, Monotonicity

Supermodular mechanism design

This paper introduces a mechanism design approach that allows dealing with the multiple equilibrium problem, using mechanisms that are robust to bounded rationality. This approach is a tool for constructing supermodular mechanisms, i.e. mechanisms that induce games with strategic complementarities. In quasilinear environments, I prove that if a social choice function can be implemented by a mechanism that generates bounded strategic substitutes - as opposed to strategic complementarities - then this mechanism can be converted into a supermodular mechanism that implements the social choice function. If the social choice function also satisfies some efficiency criterion, then it admits a supermodular mechanism that balances the budget. Building on these results, I address the multiple equilibrium problem. I provide sufficient conditions for a social choice function to be implementable with a supermodular mechanism whose equilibria are contained in the smallest interval among all supermodular mechanisms. This is followed by conditions for supermodular implementability in unique equilibrium. Finally, I provide a revelation principle for supermodular implementation in environments with general preferences.Implementation, mechanisms, learning, strategic complementarities, supermodular games