Just a bit of fun: rock-paper-scissors

So now that I have my few lines of Python written, I obviously want to have a play with it. What would happen if instead of playing Iterated Prisoner’s Dilemma, they were playing Rock Paper Scissors?

There’s no iteration here, and no chance to choose a “mixed” strategy (e.g. randomly choosing each with 1/3 probability). Just three strategies: rock, paper, scissors.

So I figured: either it’s going to go around in cycles, or converge to a point where each strategy is stuck at 1/3. Since the problem feels time-reversible I’d expect cycles. And what do we get?

It goes around in circles - each follows a sine wave, each 120 degrees out of phase from the next

(By the way, you can see them gradually spiralling outwards but I think that’s a numerical modelling issue – the discrete time steps are going to mess things up a bit).

So the next obvious question is, what about Rock Paper Scissors Lizard Spock? In case you’re not familiar, the payoffs look like this:

Rock Paper Scissors Lizard Spock
Rock 0 -1 1 1 -1
Paper 1 0 -1 -1 1
Scissors -1 1 0 1 -1
Lizard -1 1 -1 0 1
Spock 1 -1 1 -1 0

And what happens when you play them against each other in my natural selection model?

Chaotic behaviour

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