Refining Nash Implementation

Luis Corchon

Chapter 6 in The Theory of Implementation of Socially Optimal Decisions in Economics, 1996, pp 113-135 from Palgrave Macmillan

Abstract: Abstract In the two preceding chapters we have studied the Nash equilibrium approach to the problem of implementation. Various authors have put forward certain undesirable consequences of the property of monotonicity which, as you will remember, is a necessary condition for implementation in Nash equilibria. Firstly, monotonicity prohibits any type of consideration based on the cardinality of utility functions. Secondly, in some cases, distributional considerations may collide with monotonicity. The following example (taken from Moore and Repullo, 1988) will illustrate this point. We assume that there is a public good (which can take two values, 0 or 1), and a private good. The utility functions are quasi linear of the form u i = a i y + x i and the cost of 1 (resp. 0) is 1 (resp. 0). An allocation is a list (y, t 1 ,…, t n ) where y ∈ {0, 1} and t i is the tax paid by i. An economy u is a list (a i ,…, a n ) (the parameter a i is called the marginal propensity to pay). Consider an economy u for which the allocation (1, t1,…, t n ) is optimal. We now consider an economy u′ such that all the marginal propensities to pay, apart from that of the first individual, increase. Then, monotonicity implies that (1, t1,…, t n ) is also optimal for u′ no matter how much the marginal propensities to pay of all the other consumers have increased.

Keywords: Nash Equilibrium; Social Choice; Social Choice Function; Strong Equilibrium; Marginal Propensity (search for similar items in EconPapers)
Date: 1996
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pal:palchp:978-0-230-37283-2_6

Ordering information: This item can be ordered from
http://www.palgrave.com/9780230372832

DOI: 10.1057/9780230372832_6

Access Statistics for this chapter

More chapters in Palgrave Macmillan Books from Palgrave Macmillan
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().