Shared constraint in noncooperative games with economic applications
We consider generalized Nash equilibrium problems (GNEP) from structural and computational points of view. In GNEP the players' feasible sets may depend on the other players' strategies. Moreover, the players may share common constraints. We illustrate that in presence of shared constraints Nash equilibria will constitute a higher dimensional set, possibly non-closed and with boundary. This is due to in general unavoidable degeneracies for the players' parametric subproblems. Nevertheless, by assuming separability and convexity of utility functions together with linearity of shared constraints a dual approach to GNEP a la Rosen can be performed. This corresponds to solving the so-called problem of optimal resource allocation within a multi-agent environment. We model the decentralization of prices via trade or auction. We prove the optimal convergence rate of a new dual subgradient method which naturally corresponds to a process of production/price adjustments and effectively leads to a market equilibrium.
February 19, 2019 (Wednesday)
Room 205, Building E, Karlovo nám. 13
This seminar is organized by IDA research group.
Prof. Dr. Vladimir Shikhman
Professor for Economathematics, TU Chemnitz, Germany