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- Title
DISCRETIZED BEST-RESPONSE DYNAMICS FOR THE ROCK-PAPER-SCISSORS GAME.
- Authors
BEDNARIK, PETER; HOFBAUER, JOSEF
- Abstract
Discretizing a differential equation may change the qualitative behaviour drastically, even if the stepsize is small. We illustrate this by looking at the discretization of a piecewise continuous differential equation that models a population of agents playing the Rock-Paper-Scissors game. The globally asymptotically stable equilibrium of the differential equation turns, after discretization, into a repeller surrounded by an annulus shaped attracting region. In this region, more and more periodic orbits emerge as the discretization step approaches zero.
- Subjects
ROCK-paper-scissors (Game); DISCRETIZATION methods; DIFFERENTIAL equations; GAME theory; DYNAMICAL systems; GAMES of strategy (Mathematics)
- Publication
Journal of Dynamics & Games, 2017, Vol 4, Issue 1, p75
- ISSN
2164-6066
- Publication type
Article
- DOI
10.3934/jdg.2017005