Abstract:

We propose a new solution concept for generalized Nash equilibrium prob-
lems. This concept leads, under suitable assumptions, to unique solutions, which are
generalized Nash equilibria and the result of a mathematical procedure modeling the
process of finding a compromise. We first compute the favorite strategy for each player,
if he could dictate the game, and use the best response on the others’ favorite strategies
as starting point. Then, we perform a tracing procedure, where we solve parametrized
generalized Nash equilibrium problems, in which the players reduce the weight on the
best possible and increase the weight on the current strategies of the others. Finally, we
definethelimitingpoints of this tracingprocedureas solutions. Under our assumptions,
the new concept selects one reasonable out of typically infinitely many generalized
Nash equilibria.

Reference:

• Dreves, A.: How to select a solution in generalized Nash equilibrium problems. J. Optim. Theory Appl. (online 2018), DOI 10.1007/s10957-018-1327-0.