We develop benchmarks for LLM agents that act in, learn from, and strategize in unknown environments, the specifications of which the LLM agent must learn over time from deliberate exploration. Our benchmarks consist of decision-making tasks derived from key problems in economics. To forestall saturation, the benchmark tasks are synthetically generated with scalable difficulty levels. Additionally, we propose litmus tests, a new kind of quantitative measure for LLMs and LLM agents. Unlike benchmarks, litmus tests quantify differences in character, values, and tendencies of LLMs and LLM agents, by considering their behavior when faced with tradeoffs (e.g., efficiency versus equality) where there is no objectively right or wrong behavior. Overall, our benchmarks and litmus tests assess the abilities and tendencies of LLM agents in tackling complex economic problems in diverse settings spanning procurement, scheduling, task allocation, and pricing -- applications that should grow in importance as such agents are further integrated into the economy.