A Reformulation-Based Simplicial Homotopy Method for Approximating Perfect Equilibria

Yin Chen () and Chuangyin Dang ()
Additional contact information
Yin Chen: City University of Hong Kong
Chuangyin Dang: City University of Hong Kong

Computational Economics, 2019, vol. 54, issue 3, No 2, 877-891

Abstract: Abstract As a strict refinement of Nash equilibrium, the concept of perfect equilibrium was formulated by Selten (Int J Game Theory 4(1):25–55, 1975). A well-known application of this concept is that every perfect equilibrium of the agent normal form game of an extensive form game with perfect recall yields a trembling-hand perfect equilibrium (consequently a sequential equilibrium). To compute a perfect equilibrium, this paper extends Kohlberg and Mertens’s equivalent reformulation of Nash equilibrium to a perturbed game. This extension naturally leads to a homotopy mapping on the Euclidean space. With this homotopy mapping and a triangulation, we develop a simplicial homotopy method for approximating perfect equilibria. It is proved that every limit point of the simplicial path yields a perfect equilibrium. Numerical results further confirm the effectiveness of the method.

Keywords: Perfect equilibrium; Nash equilibrium; Equivalent reformulation; Homotopy mapping; Simplicial path-following method (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://link.springer.com/10.1007/s10614-018-9847-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:kap:compec:v:54:y:2019:i:3:d:10.1007_s10614-018-9847-0

Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/10614/PS2

DOI: 10.1007/s10614-018-9847-0

Access Statistics for this article

Computational Economics is currently edited by Hans Amman

More articles in Computational Economics from Springer, Society for Computational Economics Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().