MOSAIC: Dynamic Benchmarking as Mechanism Design

A benchmark scores each model on its own and ranks the scores. Those scores now decide which models get deployed and which outputs train the next round, so the leaderboard also shapes what developers build. Standalone scoring pays the same for a capability whether every other model already has it or none does. Duplicating what already scores well is then each developer's best response, and collapse onto one mode is an equilibrium: a property of the score, not of the developers. We introduce MOSAIC (Mechanism for Output Scoring that Aligns Incentives with Coverage), which pays a valid response the log-determinant volume its features add to what the record already spans: responses that the declared feature map sends to one direction, a *mode*, count as equivalent, and each further one earns less. On a shared orthogonal menu, below an explicit quality–novelty threshold, MOSAIC's equilibria are exactly the no-repeat allocations of the highest-quality modes, all of them globally optimal, where standalone scoring's unique equilibrium puts every developer on the best mode; the threshold is worst-case tight. Quality plus coverage is an exact potential: a developer's gain from replacing its own entry equals the population's gain, so every maximal improvement path ends at an equilibrium. By submodularity every such equilibrium attains at least half the optimum, and below the threshold a globally optimal population. Keeping every past response in the comparison set makes coverage grow linearly in the horizon while fresh directions remain, against standalone scoring's $\Theta (\log T)$. In separate experiments MOSAIC raises pooled effective modes from $15$ to $32$ over twelve adaptation rounds, and the gain comes from keeping the record, whether each developer keeps its own or they share one. The same mechanism raises the share of held-out tasks some developer solves by $1.4$ points at unchanged per-slot accuracy, and closes $15\%$ of the baseline-to-SOTA gap on RSI-Exam's sealed grader.