Using inverse optimization to learn cost functions in generalized Nash games

Abstract

As demonstrated by Ratliff et al. (2014), inverse optimization can be used to recover the objective function parameters of players in multi-player Nash games. These games involve the optimization problems of multiple players in which the players can affect each other in their objective functions. In generalized Nash equilibrium problems (GNEPs), a player’s set of feasible actions is also impacted by the actions taken by other players in the game. We extend the framework of Ratliff et al. (2014) to find inverse optimization solutions for a specific class of GNEPs known as jointly convex GNEPs. The resulting formulation is then applied to a simulated multi-player transportation problem on a road network. We see that our model recovers parameterizations that produce the same flow patterns as the original parameterizations and that this holds true across multiple networks, different assumptions regarding players’ perceived costs, and the majority of restrictive capacity settings and the associated numbers of players. Code for the project can be found at: https://github.com/sallen7/IO_GNEP.