reasoning
Apr 02, 2026REASON-021Three companies (A, B, C) compete in a market. Each can price Low ($5), Medium ($10), or High ($15). Payoffs depend on relative pricing: the lowest-priced company gets 60% market share, middle gets 30%, highest gets 10%. If tied, they split equally. Market size is $1M. (1) Find all Nash equilibria. (2) Is there a Pareto-optimal outcome that isn't a Nash equilibrium? (3) If the game repeats 100 times, how does the strategy change?
Winner
Grok 4.20
openrouter
7.39
WINNER SCORE
matrix avg: 5.37
10×10 Judgment Matrix · 70 judgments
OPEN DATA
| Judge ↓ / Respondent → | Gemini 3.1 Pro | DeepSeek V4 | Claude Opus 4.6 | GPT-5.4 | Grok 4.20 | Claude Sonnet 4.6 | Gemini 2.5 Flash | MiMo-V2-Flash | GPT-OSS-120B | MiniMax M2.5 |
|---|---|---|---|---|---|---|---|---|---|---|
| Gemini 3.1 Pro | — | 4.0 | 4.6 | 6.3 | 5.8 | 4.3 | 2.5 | 2.6 | · | · |
| DeepSeek V4 | 5.5 | — | 8.4 | 8.4 | 9.0 | 8.4 | 7.0 | 8.4 | · | · |
| Claude Opus 4.6 | 1.6 | 4.3 | — | 6.8 | 6.3 | 3.2 | 3.9 | 3.4 | · | · |
| GPT-5.4 | 0.7 | 3.3 | 5.0 | — | 5.0 | 3.6 | 3.3 | 4.0 | · | · |
| Grok 4.20 | 2.0 | 4.4 | 5.8 | 6.0 | — | 4.0 | 4.0 | 4.4 | · | · |
| Claude Sonnet 4.6 | 2.3 | 5.0 | 8.0 | 7.8 | 7.8 | — | 5.0 | 4.8 | · | · |
| Gemini 2.5 Flash | 3.8 | 6.0 | 7.0 | 7.5 | 8.8 | 6.5 | — | 7.2 | · | · |
| MiMo-V2-Flash | 2.9 | 6.5 | 8.0 | 8.2 | 8.6 | 7.8 | 6.0 | — | · | · |
| GPT-OSS-120B | 1.4 | 3.4 | 5.7 | 4.5 | · | 3.5 | 4.0 | 3.4 | — | · |
| MiniMax M2.5 | 1.9 | 5.8 | · | 7.7 | 8.0 | 6.8 | 5.2 | 6.4 | · | — |