A Simple and Procedurally Fair Game Form for Nash Implementation of the No-Envy Solution

2019 ◽

Vol 20 (1) ◽

Cited By ~ 1

Author(s):

Makoto Hagiwara

Keyword(s):

Nash Equilibria ◽

Simple Game ◽

Economic Behavior ◽

Allocation Problem ◽

Game Form ◽

Nash Implementation ◽

Infinitely Divisible ◽

Fair Game ◽

Game Forms

AbstractWe consider the allocation problem of infinitely divisible resources with at least three agents. For this problem, Thomson (Games and Economic Behavior, 52: 186-200, 2005) and Doğan (Games and Economic Behavior, 98: 165-171, 2016) propose “simple” but not “procedurally fair” game forms which implement the “no-envy” solution in Nash equilibria. By contrast, Galbiati (Economics Letters, 100: 72-75, 2008) constructs a procedurally fair but not simple game form which implements the no-envy solution in Nash equilibria. In this paper, we design a both simple and procedurally fair game form which implements the no-envy solution in Nash equilibria.

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On Partially Honest Nash Implementation in Private Good Economies with Restricted Domains: A Sufficient Condition

The B E Journal of Theoretical Economics ◽

10.1515/bejte-2012-0028 ◽

2013 ◽

Vol 13 (1) ◽

pp. 415-428 ◽

Cited By ~ 7

Author(s):

Ahmed Doghmi ◽

Abderrahmane Ziad

Keyword(s):

Nash Equilibria ◽

Fair Division ◽

Private Good ◽

Veto Power ◽

Sufficient Condition ◽

Game Form ◽

Nash Implementation ◽

All Solutions ◽

Restricted Domains ◽

No Veto Power

AbstractIn this article, we study the problem of Nash implementation in private good economies with single-peaked, single-plateaued, and single-dipped preferences in the presence of at least one minimally honest agent. We prove that all solutions of the problem of fair division satisfying unanimity can be implemented in Nash equilibria as long as there are at least three agents participating in the mechanism (game form). To justify this result, we provide a list of solutions which violate the condition of no-veto power.

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