Learning to adapt strategies through interaction is a key step toward more general and autonomous LLM agents. Existing approaches typically achieve behavioral adaptation by revising skill libraries. However, in multi-agent environments, opponents may simultaneously update their strategies, causing the environment itself to evolve continuously. Applying skill-revision methods designed for static environments in such settings therefore amounts to updating against an obsolete reference. To address this challenge, we introduce OASE (Opponent-Aware Selective Evolution), which identifies and adopts genuinely beneficial skill revisions in dynamic multi-agent environments. Specifically, OASE conducts paired comparisons between a candidate skill and the incumbent under identical conditions anchored by historical snapshots of opponent strategies, and adopts the candidate only when its estimated payoff gain exceeds an acceptance threshold. We evaluate OASE in two decision-making scenarios: first-price auctions and private-cost Cournot competition. Experimental results show that, compared with a Reflexion-style baseline, OASE achieves a lower final equilibrium distance in both environments while accepting substantially fewer skill revisions, thereby suppressing strategy changes that lack sufficient payoff support. OASE therefore replaces blind updating with evidence-anchored selection, allowing agents to adapt stably and efficiently even as opponents continuously evolve.

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