Teaching Nonzero Sum Games Using a Diagrammatic Determination of Equilibria

Evangelos F. Magirou - efm@aueb.gr
Department of Informatics, Athens University of Economics and Business, Patission 76, GR-104 34 Athens, Greece
Dimitrios K. Vassilakis - dkv@aueb.gr
Department of Informatics, Athens University of Economics and Business, Patission 76, GR-104 34 Athens, Greece
Ion Androutsopoulos - ion@aueb.gr
Department of Informatics, Athens University of Economics and Business, Patission 76, GR-104 34 Athens, Greece

Abstract

We present a diagrammatic method that allows the determination of all Nash equilibria of 2 x M nonzero sum games, extending thus the well known diagrammatic techniques for 2 x M zero sum and 2 x 2 nonzero sum games. We show its appropriateness for teaching purposes by analyzing modified versions of the prisoners' dilemma, the battle of the sexes, as well as of the zero sum game of matching pennies. We then use the method to give simple proofs for the existence of Nash equilibria in all 2 x M games, for both the nonzero sum (Nash existence theorem) and the zero sum case (Minimax theorem). We also prove in the same spirit the remarkable general fact that in a nondegenerate 2 x M nonzero sum game there is an odd number of equilibria.

Key words
nonzero sum games, Nash equilibrium, mixed strategy

History
Received: February 14, 2006; accepted: March 12, 2008. This paper was with the authors 1 year and 5 months for 3 revisions.

Download the PDF
10.1287/ite.8.3.115

Citation Information
Magirou, E. F., D. K. Vassilakis, I. Androutsopoulos. 2008. Teaching Nonzero Sum Games Using a Diagrammatic Determination of Equilibria. INFORMS Trans. Ed. 8(3) 115-124. Available online at http://ite.pubs.informs.org/.

DOI: 10.1287/ited.1080.0009