Invited Session Mon.2.MA 313

Monday, 13:15 - 14:45 h, Room: MA 313

Cluster 3: Complementarity & variational inequalities [...]

Optimization and equilibrium problems I


Chair: Christian Kanzow and Michael Ulbrich



Monday, 13:15 - 13:40 h, Room: MA 313, Talk 1

Oliver Stein
On differentiability properties of player convex generalized Nash equilibrium problems

Coauthors: Nadja Harms, Christian Kanzow


Any smooth generalized Nash equilibrium problem allows a reformulation as
a single constrained minimization problem with possibly nonsmooth objective
function. Under the assumption of player convexity, we study smoothness
properties of this objective function and, by using several results from
parametric optimization, we show that, except for special cases, all locally
minimal points of the reformulation are differentiability points.
This justifies a numerical approach which basically ignores the possible



Monday, 13:45 - 14:10 h, Room: MA 313, Talk 2

Alexandra Schwartz
Biased lottery versus all-pay auction contests: A revenue dominance theorem

Coauthors: Jörg Franke, Christian Kanzow, Wolfgang Leininger


We allow a contest organizer to bias a contest in a discriminatory way, that is, he can favor specific contestants through the choice of the contest success function in order to maximize the total equilibrium effort. Revenue enhancement through biasing is analyzed and compared for the two predominant contest regimes: all-pay auctions and lottery contests. In order to determine the optimally biased all-pay auction or lottery contest, the organizer has to solve a mathematical program with equilibrium constraints. We derive the optimally biased lottery contest analytically. But although this optimal lottery has a few interesting properties, it turns out that the optimally biased lottery contest will always be dominated by an appropriately biased all-pay auction.



Monday, 14:15 - 14:40 h, Room: MA 313, Talk 3

Michael Ferris
Stochastic variational inequalities and MOPEC


We describe some recent extensions of the extended mathematical programming (EMP) framework that enable the modeling of stochastic variational inequalities and link these to the notion of multiple optimization problems with equilibrium constraints (MOPEC). We show how to
incorporate stochastic information into these systems, including notions of hedging and dynamics, and give examples of their use and their possible extensions to hierarchical
modeling. We contrast these approaches to existing modeling formats such as complementarity problems and mathematical programs with equilibrium constraints, and show how this relates to decentralized operations. We demonstrate this mechanism in the context of energy and environmental planning problems, specifically for capacity expansion, hydro operation, water pricing and load shedding.


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