  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; see
Facchinei and Kanzow (2010) for more background on this problem. One example of
such impact comes in the form of joint/"coupled" constraints as referenced by
Rosen (1965), Harker (1991), and Facchinei et al. (2007) which involve other
players' variables in the constraints of the feasible region. We extend the
framework of Ratliff et al. (2014) to find inverse optimization solutions for
the class of GNEPs with joint constraints. The resulting formulation is then
applied to a simulated multi-player transportation problem on a road network.
Also, we provide some theoretical results related to this transportation
problem regarding runtime of the extended framework as well as uniqueness and
non-uniqueness of solutions to our simulation experiments. 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.
