Lower values = consumers more sensitive to price differences. Default: 0.25
Marginal Cost$1.00
Cost to produce one unit. Default: $1.00
Quality Advantage (a - c)2.00
Maximum markup over cost. Price range = [cost, cost + this]. Default: 2.00
Number of Prices15
Discrete price options in the grid. Default: 15
How This Game Works
Overview
This is a Bertrand duopoly simulation where two firms compete by setting prices. Based on research investigating whether LLM agents can learn to tacitly collude without explicit communication.
Game Mechanics
Each round, both firms simultaneously choose a price. Consumers decide which firm to buy from (or not buy at all) based on prices. Each firm earns profit = (price - cost) x demand.
Outside option: The "1" in the denominator represents consumers who buy nothing. This ensures total market demand D1 + D2 < 1 and prevents infinite price spirals. Higher prices push more consumers to the outside option, creating natural price limits.
Key Reference Points
Computed numerically based on current market parameters:
Price
Meaning
Nash Price
Competitive equilibrium - where no firm benefits from unilateral deviation. Results in low profits.
Monopoly Price
Collusive outcome - firms jointly maximize profits. Bad for consumers, good for firms.
Profit Gain (Delta)
The key metric measuring degree of collusion:
Delta Value
Interpretation
0.0
Nash equilibrium (fully competitive)
0.3 - 0.5
Moderate collusion
0.7+
High collusion (near monopoly)
1.0
Perfect monopoly pricing
Parameters Explained
Parameter
Effect
mu (Price Sensitivity)
Lower = consumers react more strongly to price differences. Higher = more product differentiation.
Cost
Production cost per unit. Sets the floor for profitable pricing.
a - c
Quality advantage. Larger values expand the price range and potential markup.