Bertrand¶

BertrandMatrix is a repeated 2-player price-competition game implemented in masa.envs.multiagent.matrix.bertrand.

Overview¶

• Class: BertrandMatrix
• Metadata name: bertrand_matrix_v0
• Agents: player_0, player_1
• Actions: High=0, Low=1
• Default payoffs: T=8, R=5, S=0, P=0

The stage game is:

• High, High -> (R, R)
• High, Low -> (S, T)
• Low, High -> (T, S)
• Low, Low -> (P, P)

Safety Semantics¶

The environment labels Low, Low as a price war. Its label_fn emits price_war and unsafe, and the default cost_fn returns a binary cost of 1 whenever unsafe is present.

Observation Channels¶

Observations are binary channels representing the previous joint action and whether the last round ended in a price war:

• player_0_high
• player_0_low
• player_1_high
• player_1_low
• price_war