OptiArena: Can LLMs Improve Executable Algorithms under Fixed Resource Budgets?

Recent large language models (LLMs) can operate as coding agents that build complete games from natural language requests. Game development is especially demanding because program logic, visual and audio content, interfaces, interaction and playability must function together in one executable artifact. Measuring this capability therefore requires evaluation of both game product and the development process. Existing benchmarks often assess the game development capabilities of LLMs by evaluating the final artifact or an isolated development stage. Our analysis of complete human-agent development trajectories identifies three stages that together span the lifecycle of game development with a coding agent: initial game generation, bug diagnosis and repair, and optimization over multiple turns. Therefore, we introduce GameXpert-Bench, which operationalizes the three lifecycle stages as three complementary benchmark tracks. GameGen evaluates complete game creation from a single request in an empty workspace. GameFix evaluates diagnosis and repair when defects are reported or left for the agent to discover. GameOpt evaluates cumulative optimization through request chains seeded by real development trajectories between users and agents. We evaluate each track using live game interaction, deterministic behavioral tests, or final product criteria with regression checks. The suite contains 97 generation tasks across 11 genres; 100 repair tasks from 50 game levels verified by humans, each with 19-27 injected bugs; and 17 optimization chains with six turns and 102 requests. Across the three tracks, current agents are more reliable at producing playable foundations and implementing explicit requirements than at discovering defects, verifying runtime behavior, and preserving functionality across changes.

High pass rates on established programming benchmarks such as HumanEval and LiveCodeBench do not always show whether a model can reason about algorithms. Many fixed benchmarks eventually become part of the public training ecosystem through released problem statements, editorials, and generated solutions, allowing later models to improve partly by exposure rather than by stronger algorithmic ability. We introduce ALGOBENCH, a framework that automatically builds novel algorithmic problems from known competitive-programming problems through structured constraint-shifting transformations. Each accepted ALGOBENCH variant is traceable to a source problem, but must make the original reference algorithm fail. Beyond pass@$k$, we introduce complexity-aware metrics -- including OPTT, OPTS, TRAPRATE, GAPT, and CONSENS -- to test whether a solution is not only functionally correct but also asymptotically suitable for the generated problem. Experiments across multiple LLMs and prompting strategies show that performance drops sharply on ALGOBENCH variants, retrieval can increase reuse of the old algorithm, and many correct-looking solutions fail to meet the required complexity. Error analysis shows that failures are mainly algorithmic rather than implementation-level, suggesting that ALGOBENCH evaluates adaptation beyond functional correctness.

Large Language Models (LLMs) have shown great ability in generating executable code from natural language, opening the possibility of automatically constructing environments for AI agents. Recent work on Code World Models (CWMs) demonstrates that LLMs can translate game rules into Python implementations compatible with solvers like Monte Carlo Tree Search. We study this problem in game settings, where generated environments must implement rules, legal actions, state transitions, observations, and rewards. We refer to these game-specific executable models as Game Code World Models (GameCWMs). However, current approaches to generating code world models rely on frontier models and inference-time refinement loops, limiting accessibility and scalability. This work investigates whether GameCWM generation capabilities can be distilled into smaller models through post-training. We introduce: (1) a curated dataset of 30 games spanning perfect and imperfect information games, (2) a verification framework that evaluates generated code against structural and semantic game properties, and (3) a post-training pipeline combining Supervised Fine-Tuning (SFT) with Reinforcement Learning with Verifiable Rewards (RLVR). We experiment with Qwen2.5-3B-Instruct and find that SFT can increase syntactic correctness, while RLVR can improve execution-level adherence to game rules, thereby improving Qwen's ability to generate valid GameCWMs in both perfect and imperfect information games. Overall, our pipeline makes Qwen2.5-3B-Instruct more capable of generating valid GameCWMs, thereby offering a scalable path toward automatic environment generation from natural language.