Computing & AI · the experiment
Put the algorithm cartel to the test
On the stage, two Q-learning agents trained together set their prices, period after period. Find the competitive price and the monopoly price yourself with the paper's demand, then test what really keeps their prices up.
1 · Find the competitive price
Same market as in the paper: two firms, a logit demand, prices between 1.43 and 1.97 for a cost of 1.
Beginner
In the paper, at what price is the collusion index 0?
Your rival always matches your price. The curve shows your profit if you alone changed yours; the white ring marks your best response. Find the price where your best response is your own price, within 0.003.
2 · Find the cartel price
Intermediate
The paper's trained pairs price at a collusion index of 0.668. With p_NE ≈ 1.473 and p_M ≈ 1.925, what is their average price?
This time, both firms change their price together. Find the common price that gives each of them the biggest profit.
3 · Cut your price for one period
The rival is frozen at the pair's price, 1.775. You cheat for a single period, as in Calvano's test.
Intermediate
This cut pays over one period. In the paper, does Calvano's one-period price cut pay overall?
Find the price cut that pays the most over this period.
4 · Raise your price instead of cutting it
Back to the pair on the stage. If its response were a punishment, it would target cheaters.
Expert
You force agent A to the monopoly price for one period: a step toward the cartel. What does the rival do, according to the paper?
5 · Switch partners
Each agent now plays against an agent from another pair, trained the same way, that it has never met.
Expert
In the paper, the collusion index then falls to 0.134. What average price, and why?
Cartel put to the test
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