Circulant Games

24 Pages Posted: 12 Sep 2014

See all articles by Georg D. Granic

Georg D. Granic

Erasmus University Rotterdam (EUR) - Department of Applied Economics

Johannes Kern

University of Cologne

Date Written: September 4, 2014


We study a class of two-player normal-form games with cyclical payoff structures. A game is called circulant if both players’ payoff matrices fulfill a rotational symmetry condition. The class of circulant games contains well-known examples such as Matching Pennies, Rock-Paper-Scissors, as well as subclasses of coordination and common interest games. The best response correspondences in circulant games induce a partition on each player’s set of pure strategies into equivalence classes. In any Nash Equilibrium all strategies within one class are either played with strictly positive or with zero probability. We further show that, strikingly, a single parameter fully determines the exact number and the structure of all Nash equilibria (pure and mixed) in these games. The parameter itself only depends on the position of the largest payoff in the first row of one of the player’s payoff matrix.

Keywords: Bimatrix Games, Circulant Games, Circulant Matrix, Number of Nash Equilibria, Rock-Paper-Scissors

JEL Classification: C70, C72, D00

Suggested Citation

Granic, Georg and Kern, Johannes, Circulant Games (September 4, 2014). Available at SSRN: or

Georg Granic

Erasmus University Rotterdam (EUR) - Department of Applied Economics ( email )


HOME PAGE: http://

Johannes Kern (Contact Author)

University of Cologne ( email )

Cologne, 50923

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics