Profit per round. Matchups use the last 30% of outer episodes. Truthful vs Truthful is the inner Hedge duel with both reports at true value. High bidder (top of each cell) · Low bidder (bottom).

✓ best / ✓ best is that bidder’s best response to the opponent’s choice — the best of Truthful, LLM, or EXP3 in that row or column. A strategy is dominant only if it is best against all three of the opponent’s strategies.

SPA
Low bidder
High bidder
Truthful
LLM
EXP3
Truthful
21.57
0.0017
12.99
0.0015
16.95✓ best
0.30✓ best
LLM
20.57
0.0012
26.34✓ best
0.0009
12.42
3.20✓ best
EXP3
23.48✓ best
0.41
21.88
0.38
15.70
1.18✓ best

SPA: no dominant strategy for the high bidder. EXP3 is dominant for the low bidder (✓ best in every row).

FPA
Low bidder
High bidder
Truthful
LLM
EXP3
Truthful
10.00
0.0053✓ best
11.56✓ best
0.0042
13.87
−0.95
LLM
10.44✓ best
0.0079
10.34
0.0116✓ best
14.02✓ best
−0.05
EXP3
9.29
0.48
11.20
0.62
10.65
0.82✓ best

FPA: no dominant strategy for either bidder. The LLM’s slight downward shade is close to truthful for the high bidder.