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2708. A New Strategy for Solving Cournot Games
Invited abstract in session MB-21: Energy sector coupling, optimization and equilibrium, stream OR in Energy.
Monday, 10:30-12:00Room: 49 (building: 116)
Authors (first author is the speaker)
1. | Nena Batenburg
|
Mathematical Sciences, University of Copenhagen | |
2. | Trine Krogh Boomsma
|
Department of Mathematical Sciences, University of Copenhagen |
Abstract
It is well known that Cournot games involving heterogeneous players with affine and decreasing demand functions and convex quadratic production cost functions can equivalently be cast as a mixed linear complementarity problem or a quadratic optimization problem (QP). Market equilibria can thus be computed using a complementarity solver or, more efficiently, a convex optimization solver. When studying such games, it is common to aggregate the consumers and substitute their inverse demand function to eliminate the market price. We argue, however, that the market price should be treated as an explicit variable that is central to the game. We show that the problem can be reformulated as a fixed-point problem (FPP) for the price only, thereby greatly reducing its dimensionality. The FPP can therefore be solved even more efficiently than the QP and also yields a more accurate solution. The FPP can be generalized to spatial games and games involving multiple commodities. We envision that this could vastly improve solution efficiency and accuracy when incorporated into dynamic or multilevel games. We finally consider a Cournot game across the markets for two commodities that may be converted into each other. The FPP formulation reveals the structure of the equilibrium and allows an analytical stability and sensitivity analysis. We find that market imperfections in either of the markets extend to the opposite market and may significantly reduce the welfare gains from market coupling.
Keywords
- Game Theory
- Mathematical Programming
- Algorithms
Status: accepted
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