MassNE: Exploring Higher-Order Interactions with Marginal Effect for Massive Battle Outcome Prediction

In online games, predicting massive battle outcomes is a fundamental task of many applications, such as team optimization and tactical formulation. Existing works do not pay adequate attention to the massive battle. They either seek to evaluate individuals in isolation or mine simple pair-wise interactions between individuals, neither of which effectively captures the intricate interactions between massive units (e.g., individuals). Furthermore, as the team size increases, the phenomenon of diminishing marginal utility of units emerges. Such a diminishing pattern is rarely noticed in previous work, and how to capture it from data remains a challenge. To this end, we propose a novel Massive battle outcome predictor with margiNal Effect modules, namely MassNE, which comprehensively incorporates individual effects, cooperation effects (i.e., intra-team interactions) and suppression effects (i.e., inter-team interactions) for predicting battle outcomes. Specifically, we design marginal effect modules to learn how units’ marginal utility changing respect to their number, where the monotonicity assumption is applied to ensure rationality. In addition, we evaluate the current classical models and provide mathematical proofs that MassNE is able to generalize several earlier works in massive settings. Massive battle datasets generated by StarCraft II APIs are adopted to evaluate the performances of MassNE. Extensive experiments empirically demonstrate the effectiveness of MassNE, and MassNE can reveal reasonable cooperation effects, suppression effects, and marginal utilities of combat units from the data.