A One-Extra Player Reduction of GNEPs to NEPs

Jointly with David Salas and Martin Schmidt

Year: 2025

Abstract: It is common opinion that generalized Nash equilibrium problems are harder than Nash equilibrium problems. In this work, we show that by adding a new player, it is possible to reduce many generalized problems to standard equilibrium problems. The reduction holds for linear problems and smooth convex problems verifying a Slater-type condition. We also derive a similar reduction for quasi-variational inequalities to variational inequalities under similar assumptions. The reduction is also obtained for purely integer linear problems. Interestingly, we show that, in general, our technique does not work for mixed-integer linear problems. The present work is built upon the recent developments in exact penalization for generalized games.

Cite as:

@techreport{Lefebvre2025OneExtra,
   title        = {A One-Extra Player Reduction of GNEPs to NEPs},
   author       = {Henri Lefebvre and David Salas and Martin Schmidt},
   year         = {2025},
   institution  = {Optimization Online},
   url          = {https://optimization-online.org/?p=32565},
   abstract     = {It is common opinion that generalized Nash equilibrium problems are harder than Nash equilibrium problems. In this work, we show that by adding a new player, it is possible to reduce many generalized problems to standard equilibrium problems. The reduction holds for linear problems and smooth convex problems verifying a Slater-type condition. We also derive a similar reduction for quasi-variational inequalities to variational inequalities under similar assumptions. The reduction is also obtained for purely integer linear problems. Interestingly, we show that, in general, our technique does not work for mixed-integer linear problems. The present work is built upon the recent developments in exact penalization for generalized games.},
   keywords     = {generalized nash equilibrium problems, nash equilibrium problems, penalization, reformulation, variational inequalities},
 }

Open Access

Optimization Online

Open Data

We did not use any data.

Open Methodology

We did not do data manipulation.

Open Source

We did not use any code.

Open Educational Resources