Replicator Cyclic Payoff Spirals
Rock beats scissors, yet cyclic competition can spiral inward, circle forever or spiral outward depending on the cost of losing.
Free theory articleRock beats scissors, yet cyclic competition can spiral inward, circle forever or spiral outward depending on the cost of losing.
Concept & interpretation
In Evolutionary Game Theory, the Replicator Dynamic models how populations of strategies evolve when successful strategies reproduce faster. Rock-Paper-Scissors provides a classic example of cyclic dominance where no single strategy is unconditionally best.
Experiment
Explore the interactive module to see how the loss magnitude and initial population affect the replicator flow. Notice that absent types remain absent on the boundaries, and the interior linearization predicts whether orbits are attracting, neutral, or repelling.
- Set Loss magnitude to a value (e.g., 0.5 for an attracting spiral).
- Set Population to a starting configuration.
- Observe the resulting vector field and interior equilibrium type in the interactive module.