Supplementary Material

Optimal Event Executions for Calculating Completion Rate When the synthesis tree becomes complicated, it is not straightforward to calculate the maximum potential executions for all the events, making it difficult to evaluate the performance through the metric Completion rate. Therefore, we develop an optimization formulation to compute the number of event executions that maximize the credits obtained by agents. This optimization is formulated in a single-agent setting. Since it aims to obtain maximum potential credits, multi-agent cases can also be applied with the set of events being the union of agents' skills. All natural resources can eventually be collected. Tab. 13 shows the parameters and variables used in this optimization. Table 13: Parameters and variables used in credit optimization. Example Prompt for LLM-C The following examples illustrate the prompts used in LLM-C for each mini-game. The prompts vary slightly for different mini-games and also differ across stages within the same mini-game. Specifically, the prompt for the dynamic scenario in Social Structure is presented in Listing 1. For the contract formation stage in Contract, the prompt is displayed in Listing 2. Similarly, the prompt for the negotiation stage in Negotiation can be found in Listing 3. The physical stage for Contract and that for Negotiation are the same. There are two physical stage settings, featuring different levels of difficulty. The corresponding prompts are provided in Listing 4 and Listing 5. Instructions: - The AdaSociety game is an open-ended multi-agent environment. The game consists of a complex crafting tree, where the agent needs to obtain as many resources as possible in the limited time and craft tools to mine more advanced resources to maximize its benefit.