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.

Additional Metadata
Keywords Bimatrix Games, Circulant Games, Circulant Matrix, Number of Nash Equilibria, Rock-Paper-Scissors
JEL Game Theory and Bargaining Theory: General (jel C70), Noncooperative Games (jel C72), Microeconomics: General (jel D00)
Persistent URL dx.doi.org/10.1007/s11238-014-9478-4, hdl.handle.net/1765/111245
Journal Theory and Decision: an international journal for multidisciplinary advances in decision sciences
Note This is an author-generated version of a research manuscript which is currently under evaluation at a journal. It is circulated exclusively for the purpose of facilitating scientific discussion. The final version of the article might differ from this one.
Citation
Granić, G.D, & Kern, J. (2015). Circulant Games. Theory and Decision: an international journal for multidisciplinary advances in decision sciences, 80(1), 43–69. doi:10.1007/s11238-014-9478-4