(A traditional folk tale of the rashunuhlist people, as told by Jessica Taylor, and literarily and mathematically adapted by the present author.)

In the days of auld lang syne on Earth-that-was, there was a population of agents playing the Nash demand game under a replicator dynamic with uniform random encounters. Whenever two agents met, each of them would name a number between 0 and 10. If the two numbers added up to 10 or less, both agents would receive of payoff of the number they named. But if the two numbers added up to more than 10, both agents would receive nothing. Agents that received higher payoffs left more descendants in the next generation, who took after their parents, as children do.

At first, the population was composed of a humble race of agents called the ceedeetee. When two of the ceedeetee met each other, each would name the number 5, and receive a payoff of 5, and all was well.

Then one day, a simple race of 9-bots invaded the land. The 9-bots would always name the number 9! When a ceedeetee agent met a 9-bot, she would reason causally: "Well, the other agent is going to name 9, so I had better name 1 if I want any payoff at all!"

And the subpopulation of 9-bots grew and grew, and the subpopulation of ceedeetee agents dwindled, until there were only one-fifth as many ceedeetee agents as there were before the 9-bot invasion.

(Because in a population with fraction $p$ ceedeetee agents, and fraction $(1 - p)$ 9-bots, the ceedeetee agents get an average payoff of $5 p + (1 - p)$ , and the 9-bots get an average payoff of $9 p$ , leading to an equilibrium at $4 p + 1 = 9 p ⟹ p = \frac{1}{5}$ with all agents receiving an average payoff of $\frac{9}{5} = 1.8$ .)

Then one day, during a meeting with her conspecific Cuhzil, a ceedeetee agent named Funk-tunul decided she had had enough.

"Why do we let these invaders take over all but a fifth of our ancestral homeland? They threaten to destroy the entire surplus of the interaction unless we name the number 1! It's extortion!" said Funk-tunul. "Surely something must be done."

"What can be done?" said Cuhzil. "All of the ceedeetee are already playing our optimal strategy when we meet a 9-bot. The 9-bot always names 9, so we always name 1—there's no way to do better."

"Perhaps," said Funk-tunul, her output channels blinking deep in thought. "Perhaps not."

"You're crazy," said Cuhzil. "Anyway, we haven't yet named the number 5 during this meeting. Are you ready?"

"A

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