Hierarchical Structures in Equilibrium Problems
|Author(s):|| RNDr. Michal Červinka Ph.D., |
|ISSN / ISBN:|
|Published in:||Doctoral thesis|
|Keywords:||MPEC, EPEC, MOPEC, M-stationarity, C-stationarity, Clarke stationarity, existence of a solution, mixed strategy, homotopy method, implicit programming approach|
|Abstract:||In the thesis we analyze equilibria of the following three conflicting situations when more than one level of decision-making process is present. If there is a single player on the upper-level we can model the situation via mathematical programs with equilibrium constraints (MPECs). When more than one-upper level decision-making player is present, these players can either act to achieve a Nash equilibrium or Pareto optimal strategy, modeled via equilibrium problems with equilibrium constraints (EPECs) or multiobjective problems with equilibrium constraints (MOPECs), respectively.
For each model, with the emphasis on EPECs and MOPECs, we derive the first order necessary optimality conditions, address the question of existence of solutions or weaker concepts of a solution and propose a suitable numerical method.