3,030 research outputs found
Deep Q-Learning for Nash Equilibria: Nash-DQN
Model-free learning for multi-agent stochastic games is an active area of
research. Existing reinforcement learning algorithms, however, are often
restricted to zero-sum games, and are applicable only in small state-action
spaces or other simplified settings. Here, we develop a new data efficient
Deep-Q-learning methodology for model-free learning of Nash equilibria for
general-sum stochastic games. The algorithm uses a local linear-quadratic
expansion of the stochastic game, which leads to analytically solvable optimal
actions. The expansion is parametrized by deep neural networks to give it
sufficient flexibility to learn the environment without the need to experience
all state-action pairs. We study symmetry properties of the algorithm stemming
from label-invariant stochastic games and as a proof of concept, apply our
algorithm to learning optimal trading strategies in competitive electronic
markets.Comment: 16 pages, 4 figure
Recommended from our members
Risk trading in capacity equilibrium models
We present a set of power investment models, the class of risky capacity equilibrium problems, reflecting different assumptions of perfect and imperfect markets. The models are structured in a unified stochastic Nash game framework. Each model is the concatenation of a model of the short-term market operations (perfect competition or Cournot), with a long-term model of investment behavior (risk neutral and risk averse behavior under different assumptions of risk trading). The models can all be formulated as complementarity problems, some of them having an optimization equivalent. We prove existence of solutions and report numerical results to illustrate the relevance of market imperfections on welfare and investment behavior. The models are constructed and discussed as two stage problems but we show that the extension to multistage is achieved by a change of notation and a standard assumption on multistage risk functions. We also treat a large multistage industrial model to illustrate the computational feasibility of the approach
An SLSPP-algorithm to compute an equilibrium in an economy with linear production technologies
Topology
Complexity Theory, Game Theory, and Economics: The Barbados Lectures
This document collects the lecture notes from my mini-course "Complexity
Theory, Game Theory, and Economics," taught at the Bellairs Research Institute
of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th
McGill Invitational Workshop on Computational Complexity.
The goal of this mini-course is twofold: (i) to explain how complexity theory
has helped illuminate several barriers in economics and game theory; and (ii)
to illustrate how game-theoretic questions have led to new and interesting
complexity theory, including recent several breakthroughs. It consists of two
five-lecture sequences: the Solar Lectures, focusing on the communication and
computational complexity of computing equilibria; and the Lunar Lectures,
focusing on applications of complexity theory in game theory and economics. No
background in game theory is assumed.Comment: Revised v2 from December 2019 corrects some errors in and adds some
recent citations to v1 Revised v3 corrects a few typos in v
Optimal GENCO bidding strategy
Electricity industries worldwide are undergoing a period of profound upheaval. The conventional vertically integrated mechanism is being replaced by a competitive market environment. Generation companies have incentives to apply novel technologies to lower production costs, for example: Combined Cycle units. Economic dispatch with Combined Cycle units becomes a non-convex optimization problem, which is difficult if not impossible to solve by conventional methods. Several techniques are proposed here: Mixed Integer Linear Programming, a hybrid method, as well as Evolutionary Algorithms. Evolutionary Algorithms share a common mechanism, stochastic searching per generation. The stochastic property makes evolutionary algorithms robust and adaptive enough to solve a non-convex optimization problem. This research implements GA, EP, and PS algorithms for economic dispatch with Combined Cycle units, and makes a comparison with classical Mixed Integer Linear Programming.;The electricity market equilibrium model not only helps Independent System Operator/Regulator analyze market performance and market power, but also provides Market Participants the ability to build optimal bidding strategies based on Microeconomics analysis. Supply Function Equilibrium (SFE) is attractive compared to traditional models. This research identifies a proper SFE model, which can be applied to a multiple period situation. The equilibrium condition using discrete time optimal control is then developed for fuel resource constraints. Finally, the research discusses the issues of multiple equilibria and mixed strategies, which are caused by the transmission network. Additionally, an advantage of the proposed model for merchant transmission planning is discussed.;A market simulator is a valuable training and evaluation tool to assist sellers, buyers, and regulators to understand market performance and make better decisions. A traditional optimization model may not be enough to consider the distributed, large-scale, and complex energy market. This research compares the performance and searching paths of different artificial life techniques such as Genetic Algorithm (GA), Evolutionary Programming (EP), and Particle Swarm (PS), and look for a proper method to emulate Generation Companies\u27 (GENCOs) bidding strategies.;After deregulation, GENCOs face risk and uncertainty associated with the fast-changing market environment. A profit-based bidding decision support system is critical for GENCOs to keep a competitive position in the new environment. Most past research do not pay special attention to the piecewise staircase characteristic of generator offer curves. This research proposes an optimal bidding strategy based on Parametric Linear Programming. The proposed algorithm is able to handle actual piecewise staircase energy offer curves. The proposed method is then extended to incorporate incomplete information based on Decision Analysis. Finally, the author develops an optimal bidding tool (GenBidding) and applies it to the RTS96 test system
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