Equilibrium problems representing interaction in physical environments typically require continuous strategies which satisfy opponent-dependent constraints, such as those modeling collision avoidance. However, as with finite games, mixed strategies are often desired, both from an equilibrium existence perspective as well as a competitive perspective. To that end, this work investigates a chance-constraint-based approach to coupled constraints in generalized Nash equilibrium problems which are solved over pure strategies and mixing weights simultaneously. We motivate these constraints in a discrete setting, placing them on tensor games ($n$-player bimatrix games) as a justifiable approach to handling the probabilistic nature of mixing. Then, we describe a numerical solution method for these chance constrained tensor games with simultaneous pure strategy optimization. Finally, using a modified pursuit-evasion game as a motivating examples, we demonstrate the actual behavior of this solution method in terms of its fidelity, parameter sensitivity, and efficiency.

翻译：在物理环境中表征互动的均衡问题通常需要满足对手相关约束（如避碰建模）的连续策略。然而，与有限博弈类似，无论从均衡存在性视角还是竞争性视角来看，混合策略通常都是必要的。为此，本研究探讨了一种基于机会约束的方法，用于处理广义纳什均衡问题中同时求解纯策略和混合权重的耦合约束。我们在离散设定中推导这些约束，将其应用于张量博弈（$n$ 人双矩阵博弈）作为处理混合概率性质的合理方法。随后，我们描述了带同步纯策略优化的机会约束张量博弈的数值求解方法。最后，通过改进的追逃博弈作为典型案例，我们展示了该方法在保真度、参数敏感性和效率方面的实际表现。