Abstract In this paper, robust optimization methodologies for solving incomplete-information two-person zero-sum and nonzero-sum games are developed that consider single or multiple interval inputs (i.e., interval-valued payoffs). Unlike complete-information games, where all parameters of the game such as individual players’ payoffs are assumed common knowledge, incomplete-information games deal with uncertain payoffs. In some cases, the payoffs may be estimated from imprecise data, such as interval data. In such situations, conventional methods that use deterministic payoffs are not appropriate. Also, in many cases, payoffs are available as multiple intervals. This paper proposes robust optimization models for non-cooperative, simultaneous-move, one-shot, two-person games with incomplete information. The proposed approaches are able to aggregate information from multiple sources and thereby result in more realistic outcomes. The robust optimization methods developed in this paper can be used to solve two-person games with interval-valued (single or multiple intervals) payoffs as well as with single-valued (i.e., deterministic) and aleatory (i.e., precise probabilistic information) payoffs or a combination of them. The proposed methodologies are illustrated with several example problems including an investment decision problem and a capacity expansion decision problem. The proposed decoupled approach is compared with some previously developed approaches and it is demonstrated that the proposed formulations generate conservative solutions in the presence of interval uncertainty.

中文翻译：

---

一种求解区间不确定下两人博弈的鲁棒优化方法

摘要 在本文中，开发了用于解决不完全信息两人零和和非零和博弈的稳健优化方法，这些博弈考虑了单个或多个区间输入（即区间值支付）。与完全信息博弈不同，在完全信息博弈中，博弈的所有参数（例如个体玩家的收益）都被假定为常识，而不完全信息博弈则处理不确定的收益。在某些情况下，可能会根据不精确的数据（例如区间数据）估计收益。在这种情况下，使用确定性收益的传统方法是不合适的。此外，在许多情况下，收益可作为多个区间使用。本文针对信息不完全的非合作、同时移动、单次、两人游戏提出了稳健的优化模型。所提出的方法能够汇总来自多个来源的信息，从而产生更现实的结果。本文中开发的稳健优化方法可用于解决具有区间值（单或多区间）收益以及单值（即确定性）和随机（即精确概率信息）收益的两人博弈或它们的组合。所提出的方法通过几个示例问题进行说明，包括投资决策问题和产能扩张决策问题。将所提出的解耦方法与一些先前开发的方法进行比较，并证明所提出的公式在存在区间不确定性的情况下生成了保守的解决方案。