Supplementary Material

Tab. 13 shows the parameters and variables used in this optimization. Table 13: Parameters and variables used in credit optimization.Known Parameters Description ϱ = R Eq. 5 presents the optimization formulation, where Eq. 5a calculates the total credits gained by the 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. The corresponding prompts are provided in Listing 4 and Listing 5. 27 Listing 1: Prompt example for dynamic scenario in Social Structure . Instructions: - The AdaSociety game is an open-ended multi-agent environment. The game consists ofa complex crafting tree, where the agent needs to obtain as many resources aspossible in the limited time and craft tools to mine more advanced resources tomaximize its benefit. At the same time, agents can also take other actions tohelp them increase their returns. The numbers of resources are limited.- Map: AdaSociety is a 2D grid-world game. The map size is 15*15.- Some of them can only bediscovered with some specific tools, which will be introduced next.-