Interactive environments offer a practical way to evaluate large language model (LLM) agents, and competitive games extend this evaluation to decisions shaped by competing goals and other agents' choices. Yet existing evaluations confined to individual games or execution frameworks leave unclear which competitive advantages persist across settings. We introduce DECE (Diverse Eurogame Competitive Environments), a unified arena spanning ten Eurogames with shared interfaces and evaluation protocols. These games combine lasting strategic commitments, competition over shared resources, and multiple routes to victory. Our primary study evaluates 12 model-harness configurations, spanning nine models and four execution harnesses, in 480 three-player matches across ten games. The main and supplementary studies comprise 1,032 completed matches in total. These comparisons reveal broad cross-game ranking agreement alongside game-specific strengths. Matched studies show that the same model can perform differently across execution harnesses, adding another source of variation to these profiles. These performance advantages do not consistently translate into better token or cost efficiency, making resource use an additional consideration when comparing configurations. Together, the findings support evaluating complete agent configurations by both their competitive performance across games and the resources needed to achieve it.
Yan Zhang, Jiong Tuo, Meng Ding, Yuheng Ma, Di Wang
Sparse linear regression is a fundamental problem in high-dimensional statistics, and its private counterparts leave a large gap between the central and the local model of differential privacy. Shuffled differential privacy (SDP) sits between the two, offering accuracy closer to the central model without the trust requirement of a central curator. This paper studies sparse linear regression under both non-interactive and interactive SDP protocols. In the non-interactive setting, any non-interactive $(ε,δ)$-SDP protocol is shown to incur an $\ell_2$-norm estimation error of $Ω( \frac{\sqrt{dk}}{nε} )$ with dimension $d$, sparsity $k$, and $n$ users, revealing an inherent dimensionality barrier. In addition, a non-interactive algorithm is proposed that achieves an $\ell_2$-norm upper bound of $\tilde{\mathcal{O}}( \sqrt{\frac{k}{n}} + \frac{d\sqrt{k}}{nε})$. To overcome this barrier, we turn to the interactive user-level setting, where each user holds $m$ samples. A two-round interactive algorithm is developed that first recovers the support through a heavy hitter step and then estimates the parameter, achieving an error of $\tilde{\mathcal{O}}( \sqrt{\frac{k}{nm}} + \frac{k}{n\sqrt{m}ε} )$ with no polynomial dependence on $d$. Furthermore, by extending the score attack framework to user-level data, a new lower bound $Ω( \sqrt{\frac{k\log(d/k)}{nm}} + \frac{k\log(d/k)}{n\sqrt{m}ε} )$ is established for any user-level $(ε,δ)$-DP, showing that the proposed algorithm is near-optimal with only a gap of the factor $\log(d/k)$.