Effects of Edge Marking and Initial Strategy Distributions on ESS Formation in the Multi-Player Prisoner’s Dilemma through an LMM-Assisted Simulation

We analyze how spatial structure and initial strategy distributions shape the evolutionary stability of cooperation (ESS) in repeated multi-player Prisoner’s Dilemma, using simulations where a large multimodal model (LMM) serves as a research tool (for automation, code generation, and visualization), not as a player. On 2D/3D polyomino tilings, we manipulate the anisohedral number (��) and edge marking, and observe dynamics under rule-based strategies (C/D/TFT) with a best-performing-neighbor imitation update rule. Results show: (1) Structural factors (anisohedrality, edge marking) outweigh initial strategy shares in determining cooperative stability. In particular, edge marking markedly reduces rounds-to-ESS within each ��, with very large effect sizes (Hedges’ ��) (2) Higher �� leads to longer time to ESS, indicating that strategy diversity and spatial differentiation support sustained cooperation. We propose an AI-assisted experimental template applicable to mathematical modeling and strategic reasoning tasks. A limitation is the lack of qualitative evidence on learners’ cognition and strategy formation; classroom-based validation is warranted.