Mathematics – Optimization and Control
Scientific paper
2011-02-14
Mathematics
Optimization and Control
Scientific paper
A function $u: X\to\mathbb{R}$ defined on a partially ordered set is quasi-Leontief if, if for all $x\in X$, the upper level set $\{x^\prime\in X: u(x^\prime)\geqslant u(x)\} $ has a smallest element. A function $u: \prod_{j=1}^nX_j\to\mathbb{R}$ whose partial functions obtained by freezing $n-1$ of the variables are all quasi-Leontief is an individually quasi-Leontief function; a point $x$ of the product space is an efficient point for $u$ if it is a minimal element of $\{x^\prime\in X: u(x^\prime)\geqslant u(x)\} $. Part I deals with the maximisation of quasi-Leontief functions and the existence of efficient maximizers. Part II is concerned with the existence of efficient Nash equilibria for abstract games whose payoff functions are individually quasi-Leontief. Order theoretical and algebraic arguments are dominant in the first part while, in the second part, topology is heavily involved. In the framework and the language of tropical algebras, our quasi-Leontief functions are the additive functions defined on a semimodule with values in the semiring of scalars.
Briec Walter
Horvath Charles
Liang QiBin
No associations
LandOfFree
Quasi-Leontief utility functions on partially ordered sets I: efficient points does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quasi-Leontief utility functions on partially ordered sets I: efficient points, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quasi-Leontief utility functions on partially ordered sets I: efficient points will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-215300