Abstract

In this paper, we study the Nash implementation in an allocation problem with single-dipped preferences. We show that, with at least three agents, Maskin monotonicity is necessary and sufficient for implementation. We examine the implementability of various social choice correspondences (SCCs) in this environment, and prove that some well-known SCCs are Maskin monotonic ( but they do not satisfy no-veto power) and hence Nash implementable.

Highlights

  • The objective of implementation theory is to study, in a rigorous manner, the relationship between outcomes in a society and the institutions under which those outcomes arise

  • We show that strict monotonicity is sufficient, but is necessary, as long as it becomes equivalent to Maskin monotonicity

  • We provide in the subsection a list of solutions which satisfy Maskin monotonicity, and violate the condition of no-veto power

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Summary

Introduction

The objective of implementation theory is to study, in a rigorous manner, the relationship between outcomes in a society and the institutions under which those outcomes arise. Manjunath [27] explored the problem of locating a single public good when preferences of agents are single-dipped, providing a characterization of all rules satisfying unanimity and strategy-proofness properties. With at least three agents, any solution of the problem of fair division can be implemented in Nash equilibria if—and only if—it satisfies Maskin monotonicity Via this result, the no-veto power condition is dispensed of in this area, and so we implement some well-known correspondences which satisfy Maskin monotonicity but violate the condition of no-veto power. In. Section 3, we state and prove our main result in a domain of the allocation problem with single-dipped preferences, and we justify this result providing some well-known correspondences which satisfy Maskin monotonicity and violate the no-veto power condition.

General Notations and Definitions
Applications to Allocation Problem with Single-Dipped Preferences
The Main Result
Maskin Monotonicity
No-Veto Power
Conclusion
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