Pure Nash Equilibrium
The ability to play a best response strategy when given knowledge that another agent is also best responding (i.e., is rational). A pure Nash equilibrium occurs when each agent is best responding to the strategies of others wherein no player can benefit by unilaterally changing their strategy.
Sparkle Wash and Shine Station are the only two car washes at a suburban highway exit. Each can charge either price low or price high per car wash. The two differ in location and reputation, so they do not sell the same amounts. The number of washes each sells per week depends on both prices. If both charge price high, Sparkle Wash sells a hh washes and Shine Station sells b hh. If Sparkle Wash charges price high and Shine Station charges price low, Sparkle Wash sells a hl and Shine Station sells b hl. If Sparkle Wash charges price low and Shine Station charges price high, Sparkle Wash sells a lh and Shine Station sells b lh. If both charge price low, Sparkle Wash sells a ll and Shine Station sells b ll. Costs are negligible, so each one's profit is its price times the number of washes it sells, and each wants to maximise its own profit. In the pure-strategy Nash equilibrium of this pricing game, what price does Sparkle Wash charge?
Use it
from datasets import load_dataset
ds = load_dataset("narunraman/steer", "pure_nash")curl "https://steer-benchmark.cs.ubc.ca/api/sample?element_name=pure_nash&n=5&seed=42"
See the Reference for the parameters.