Abstract
In this chapter, we study 2-person normal form games, zero-sum games ( matrix games ) as well as nonzero-sum games ( bimatrix games ). It is our objective to investigate whether for this special class of games the results of the previous chapter can be refined and specialized.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes
An algorithm to find a perfect equilibrium in a bimatrix game has been described in Van den Elzen and Talman [1991]. The structure of the set of perfect equilibria of bimatrix games is investigated in Borm et al. [1988]. It is shown in that paper that the structure of this set resembles that of the Nash equilibrium set (see Theorem 3.3.1). Borm [1990] studies the class of 2 × n games in detail. In addition to showing how one can find all perfect and all proper equilibria, he characterizes stable sets and persistent retracts. He finds that stable sets consist of either one or two perfect equilibria, that each stable component contains a proper equilibrium, and that each persistent equilibrium is perfect.
Also see Krohn et al. [1989].
An alternative (equivalent) definition of regularity in bimatrix games is given in Jansen [1987].
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
van Damme, E. (1991). 3 Matrix and Bimatrix Games. In: Stability and Perfection of Nash Equilibria. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58242-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-58242-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53800-4
Online ISBN: 978-3-642-58242-4
eBook Packages: Springer Book Archive