Cyclic dominance in a 2-person Rock-Scissors-Paper game

Liliana Garrido-da-Silva, Sofia B. S. D. Castro

Published 2016-07-29Version 1

The Rock-Scissors-Paper game has been studied in the context of single population dynamics to account for cyclic behaviour. We use a 2-person parametrised version of this game to illustrate how cyclic behaviour is still a dominant feature of the dynamics. The cyclic behaviour is observed near a heteroclinic cycle with two nodes such that, at each node, players alternate in winning and losing. This cycle is shown to be as stable as possible for a wide range of parameter values. The parameters are related to the players' payoff when a tie occurs. This cycle is part of a heteroclinic network: there are two other cycles with two nodes and two cycles with three nodes. The cycles with two nodes exhibit some intermediate stability for a large subset of parameter space, contained in the complement of the set of stability of the first cycle. These two-node cycles represent oscillations between a tie between players and a win for only one of the players. The three-node cycles are always unstable and describe a cycle among all possible outcomes in the game, in the two possible sequences. Using some applications to price setting models, we propose what could be a starting point for the contribution of the Rock-Scissors-Paper game to the understanding of cyclic dominance in two-player games.