Using EPECs to model bilevel games in restructured electricity markets with locational prices

CWPE0619 (EPRG0602) Xinmin Hu and Daniel Ralph (Feb 2006) Using EPECs to model bilevel games in restructured electricity markets with locational prices We study a bilevel noncooperative game-theoretic model of electricity markets with locational marginal prices. Each player faces a bilevel optimization problem that we remodel as a mathematical program with equilibrium constraints, MPEC. This gives an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for existence of pure strategy Nash equilibria for this class of bilevel games and give some applications. We show by examples the effect of network transmission limits, i.e. congestion, on existence of equilibria. Then we study, for more general EPECs, the weaker pure strategy concepts of local Nash and Nash stationary equilibria. We model the latter via complementarity problems, CPs. Finally, we present numerical examples of methods that attempt to find local Nash or Nash stationary equilibria of randomly generated electricity market games. The CP solver PATH is found to be rather effective in this context

Tolling, collusion and equilibrium problems with equilibrium constraints

An Equilibrium Problem with an Equilibrium Constraint (EPEC) is a mathematical construct that can be applied to private competition in highway networks. In this paper we consider the problem of finding a Nash Equilibrium in a situation of competition in toll pricing on a network utilising two alternative algorithms. In the first algorithm, we utilise a Gauss Seidel fixed point approach based on the cutting constraint algorithm for toll pricing. The second algorithm that we propose, a novel contribution of this paper, is the extension of an existing sequential linear complementarity programming approach for finding the competitive Nash equilibrium when there is a lower level equilibrium constraint. Finally we develop an intuitive approach to represent collusion between players and demonstrate that as the level of collusion goes from none to full collusion so the solution maps from the Nash to monopolistic solution. However we also show that there may be local solutions for the collusive monopoly which lie closer to the second best welfare toll solution than does the competitive Nash equilibrium

An Exact Solution Method for Binary Equilibrium Problems with Compensation and the Power Market Uplift Problem

We propose a novel method to find Nash equilibria in games with binary decision variables by including compensation payments and incentive-compatibility constraints from non-cooperative game theory directly into an optimization framework in lieu of using first order conditions of a linearization, or relaxation of integrality conditions. The reformulation offers a new approach to obtain and interpret dual variables to binary constraints using the benefit or loss from deviation rather than marginal relaxations. The method endogenizes the trade-off between overall (societal) efficiency and compensation payments necessary to align incentives of individual players. We provide existence results and conditions under which this problem can be solved as a mixed-binary linear program. We apply the solution approach to a stylized nodal power-market equilibrium problem with binary on-off decisions. This illustrative example shows that our approach yields an exact solution to the binary Nash game with compensation. We compare different implementations of actual market rules within our model, in particular constraints ensuring non-negative profits (no-loss rule) and restrictions on the compensation payments to non-dispatched generators. We discuss the resulting equilibria in terms of overall welfare, efficiency, and allocational equity

Is Everything Neutral?

In his well-known analysis of the national debt, Robert Barro introduced the notion of a "dynastic family." This notion has since become a standard research tool, particularly in the areas of public finance and macroeconomics. In this paper, we critique the assumptions upon which the dynastic mode1 is predicated, and argue that this framework is not a suitable abstraction in contexts where the objective is to analyze the effects of public policies. We reach this conclusion by formally considering a world in which each generation consists of a large number of distinct individuals, as opposed to one representative individual. We point out that family linkages form complex networks, in which each individual may belong to many dynastic groupings. The resulting proliferation of linkages between families gives rise to a host of neutrality results, including the irrelevance of all public redistributions, distortionary taxes, and prices. Since these results are not at all descriptive of the real world, we conclude that, in some fundamental sense, the world is not even approximately dynastic. These observations call into question all policy related results based on the dynastic framework, including the Ricardian equivalence hypo thesis.

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Recent advances in multiobjective convex semi-infinite optimization

This paper reviews the existing literature on multiobjective (or vector) semi-infinite optimization problems, which are defined by finitely many convex objective functions of finitely many variables whose feasible sets are described by infinitely many convex constraints. The paper shows several applications of this type of optimization problems and presents a state-of-the-art review of its methods and theoretical developments (in particular, optimality, duality, and stability)

Modeling of Competition and Collaboration Networks under Uncertainty: Stochastic Programs with Resource and Bilevel

We analyze stochastic programming problems with recourse characterized by a bilevel structure. Part of the uncertainty in such problems is due to actions of other actors such that the considered decision maker needs to develop a model to estimate their response to his decisions. Often, the resulting model exhibits connecting constraints in the leaders (upper-level) subproblem. It is shown that this problem can be formulated as a new class of stochastic programming problems with equilibrium constraints (SMPEC). Sufficient optimality conditions are stated. A solution algorithm utilizing a stochastic quasi-gradient method is proposed, and its applicability extensively explained by practical numerical examples