Efficiency in symmetric 2 × 2 games

Gunderson, Ellie; Roberts, David P.

doi:10.2140/involve.2024.17.795

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-4184 (online)

ISSN 1944-4176 (print)

Author index

To appear

Other MSP journals

Efficiency in symmetric $2 \times 2$ games

Ellie Gunderson and David P. Roberts

Vol. 17 (2024), No. 5, 795–834

DOI: 10.2140/involve.2024.17.795

Abstract

We describe in detail the triangulated sphere introduced by Goforth and Robinson to parametrize symmetric $2 \times 2$ games. Next we measure, via an efficiency function on this sphere with values in $[0, 1]$ , the extent to which equilibrium play obtains the large returns that are obtained by cooperative play. Finally, we discuss ways of improving efficiency.

Keywords

symmetric game, equilibrium, efficiency

Mathematical Subject Classification

Primary: 91A70

Secondary: 91A05, 91A11

Milestones

Received: 18 April 2023

Revised: 1 June 2023

Accepted: 3 July 2023

Published: 21 November 2024

Communicated by Kenneth S. Berenhaut

Authors

Ellie Gunderson
Department of Geography University of Minnesota, Twin Cities Minneapolis, MN United States

David P. Roberts
Division of Science and Mathematics University of Minnesota, Morris Morris, MN United States

Vol. 17, No. 5, 2024