Profit per round, last 30% of each episode. High bidder (top of each cell) · Low bidder (bottom).

✓ best / ✓ best is that bidder’s best response to the opponent’s choice — the better of LLM vs Hedge in that row or column. A strategy is dominant only if it is best against both of the opponent’s strategies.

SPA
Low bidder
High bidder
LLM
Hedge
LLM
38.38✓ best
0.00
15.45
5.85✓ best
Hedge
14.97
0.55✓ best
22.26✓ best
0.19

SPA: no dominant strategy for either bidder, and no cell is a mutual best response (no cell has ✓ on both lines).

FPA
Low bidder
High bidder
LLM
Hedge
LLM
9.32
1.27
0.17
10.79✓ best
Hedge
15.63✓ best
0.75
11.69✓ best
2.35✓ best

FPA: Hedge is dominant for both bidders (✓ best in every column for high, every row for low). Hedge/Hedge is the mutual best response.