Existence of Equilibrium Points in Non-Product Spaces

An equilibrium point in game theory is a situation where a unilateral change by only one of the players does not yield an increase of his profit or "payoff" function. In this paper it will be shown that an equilibrium point exists if: the payoff functions are continuous in all the variable...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on applied mathematics 1966-01, Vol.14 (1), p.181-190
Main Author: Ponstein, J.
Format: Article
Language:English
Subjects:
Concavity
Convexity
Diagonal lemma
Equilibrium
Euclidean space
Game theory
Mathematical functions
Mathematical vectors
Nash equilibrium
Polyhedrons
Variables
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:An equilibrium point in game theory is a situation where a unilateral change by only one of the players does not yield an increase of his profit or "payoff" function. In this paper it will be shown that an equilibrium point exists if: the payoff functions are continuous in all the variables and are concave in the variables belonging to each relevant player, the region in which the game is played is closed, bounded and convex and satisfies a weak continuity condition. The continuity condition is automatically satisfied if the region is a convex polyhedron. It is not assumed that the region in which the game is played is the product space of the subregions of each individual player. Therefore, the existence of an equilibrium point is shown for the general case of the so-called "mixed constraints".
ISSN:0036-1399
1095-712X
DOI:10.1137/0114015