Figure 3

Rock-Paper-Scissors Theory and Simulations.

Our main distance result is consistent with a large class of learning models. (A): In the replicator dynamic, the average distance converges toward the center when a = 4 (right), cycles indefinitely at a fixed distance when a = 2 (middle), or diverges away from the center when a = 1.1 (left), yielding a larger average distance in a = 1.1 than a = 4. The arrows are solutions to the ordinary differential equation³³. (B): Stochastic simulations of reinforcement learning likewise give results similar to our experimental data; as in our experimental data, population distributions farther from the center are more frequent when a = 1.1 than when a = 2 and a = 4. The bubbles correspond to population distributions of rock paper scissors observed in 5 simulation runs of two versions of reinforcement learning simulations meant to follow Frequency Feedback and Payoff Feedback, respectively. The construction of this plot is identical to Figure 2 except it is based on the simulation data instead of the experimental data and is based on the same number of distinct choices (see Supplementary Information for a description of the simulation).