Operational algorithms for solving the inverse problem for the graph model for conflict resolution are presented for the case of two decision makers (DMs) under a variety of solution concepts, including Nash stability (Nash), general metarationality (GMR), symmetric metarationality (SMR), and sequential stability (SEQ). The algorithms based on integer programming enable a DM, an analyst, or a mediator to obtain all of the preferences required to make a specified state to be an equilibrium or resolution. For the cases of Nash, GMR, and SMR, the respective inverse algorithm for the focal DM is formulated as a 0–1 integer linear programming problem even when both DMs’ preferences are unknown. For the situation of SEQ, when both DMs’ preferences are unknown, the focal DM’s algorithm is a 0–1 integer nonlinear programming problem while, under the condition that the opponent’s preferences are known, the focal DM’s 0–1 integer programming problem is linear. The usefulness of the algorithms developed is demonstrated by applying them to an illustrative dispute.

针对两个决策者 (DM) 在各种解决方案概念下，包括纳什稳定性 (Nash)、一般元理性 (GMR)、对称元理性 (SMR)，提出了用于解决冲突解决图模型的逆问题的运算算法) 和顺序稳定性 (SEQ)。基于整数规划的算法使 DM、分析师或调解人能够获得使特定状态成为平衡或解决方案所需的所有偏好。对于 Nash、GMR 和 SMR 的情况，即使两个 DM 的偏好未知，焦点 DM 的各自逆算法也被公式化为 0-1 整数线性规划问题。对于 SEQ 的情况，当两个 DM 的偏好未知时，焦点 DM 的算法是一个 0-1 整数非线性规划问题，而，在已知对手偏好的条件下，焦点DM的0-1整数规划问题是线性的。所开发算法的实用性通过将它们应用于说明性争议来证明。