“The mixed Nash equilibrium strategy would clearly be for each player to play all three options with 1/3 possibility. In a repeated number of trials, one would expect to see about as many rocks played as paper and scissors. Similarly, in the lizard populations that have all three mating types, the relative frequency of the three male types is about even in the long-term (although it fluctuates in the short-term).
How is this maintained? Although the rock-paper-scissors analogy is useful, the lizards don’t look at the current situation in their area and decide which form to take. Rather, their appearance and behavior is more-or-less hard-coded into their DNA. This is where evolution comes into play. ‘Winning’ the mating ‘game’ means having offspring, which means more males of your mating type. So any situation which is favorable to a particular mating type will lead to that mating type become more prevalent in the subsequent generation. In this way, balance is maintained. Are there more oranges than balance would indicate, and not enough yellows? Then the yellows will be more successful, since there are more oranges to beat, and the next generation will have more yellows and fewer oranges.”
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