A Regularized Nikaido-Isoda Function Approach to Multi-Leader-Follower Games

Mathematics > Optimization and Control [Submitted on 18 Jun 2026] Title:A Regularized Nikaido-Isoda Function Approach to Multi-Leader-Follower Games View PDF HTML (experimental)Abstract:A multi-leader--follower game (MLFG) is a hierarchical noncooperative game in which leaders compete at the upper level while taking into account the followers' best responses at the lower level. A typical approach to solving the MLFG reformulates it as an equilibrium problem with equilibrium constraints (EPECs) by replacing the lower-level game with its KKT conditions. Another approach, when each follower's response is unique, is to reformulate the MLFG as a Nash equilibrium problem by substituting these response functions into each leader's problem. However, both reformulations may lack scalability since higher-order derivatives may be required when solving the resulting problems. In this paper, we propose a new reformulation of the MLFG by exploiting a regularized Nikaido--Isoda function and approximating the MLFG by a single-level differentiable Nash equilibrium problem with a penalty parameter. The proposed reformulation neither requires derivative information on the followers' game nor assumes convexity of each follower's problem; hence, it can handle a broader class of MLFGs. Under global subanalyticity, we analyze the mathematical relationship between equilibria of the original MLFG and the proposed reformulation. References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.