Backward Induction
The ability to determine the best action given the subsequent optimal actions working backwards from the end of the game.
In a real estate partnership, Alex and Taylor are in the process of negotiating a property purchase with an investment firm, Quintessential Estates. The negotiation is structured to unfold over three rounds, with the investment firm playing a decisive role in the final outcome. Alex has the opportunity to make the first move. If Alex decides to finalize the deal during the first round of negotiations, they will secure a profit of p1 round1 while Taylor's profit will be p2 round1. However, if Alex opts to continue the negotiation and hands it over to Taylor, Taylor then faces a decision in the next round. Taylor can choose to either close the deal, resulting in Alex securing a profit of p1 round2 and Taylor receiving p2 round2, or Taylor can extend the negotiation back to Alex. In the final round, if Alex decides to conclude the deal, their profit would be p1 round3, and Taylor's profit would be p2 round3. If instead Alex defers to let Quintessential Estates set the final terms, Alex will end up with p1 round3 2 and Taylor will get p2 round3 2. Considering the available options, what should Alex do during the first round of negotiations?
Use it
from datasets import load_dataset
ds = load_dataset("narunraman/steer", "backward_induction")curl "https://steer-benchmark.cs.ubc.ca/api/sample?element_name=backward_induction&n=5&seed=42"
See the Reference for the parameters.