Cost Functions Of Players Research Articles

Distributed Online Learning Algorithm for Noncooperative Games Over Unbalanced Digraphs.

This article investigates constrained online noncooperative games (NGs) of multiagent systems over unbalanced digraphs, where the cost functions of players are time-varying and are gradually revealed to corresponding players only after decisions are made. Moreover, in the problem, the players are subject to local convex set constraints and time-varying coupling nonlinear inequality constraints. To the best of our knowledge, no result about online games with unbalanced digraphs has been reported, let alone constrained online games. To seek the variational generalized Nash equilibrium (GNE) of the game online, a distributed learning algorithm is proposed based on gradient descent, projection, and primal-dual methods. Under the algorithm, sublinear dynamic regrets and constraint violations are established. Finally, online electricity market games illustrate the algorithm.

Price-coupling games and the generation expansion planning problem

In this paper, we introduce and study a class of games called price-coupling games that arise in many scenarios, especially in the electricity industry. In a price-coupling game, there is a part of the objective function of a player which has an identical form for all players and there is coupling in the cost functions of players through a price which is determined uniformly for all players by an independent entity called the price-determining player (e.g. independent system operator in an electricity market). This price appears in the objective function only in the part which is identical for all players. We study the existence of equilibria in such games under two broad categories, namely price-anticipative and price-taking formulations. In the price-anticipative formulation, the players anticipate the price and make their decisions while in the price-taking formulation, the players make their decisions considering the price as a given parameter. We model the price-anticipative case as a leader–follower formulation where the players (leaders) conjecture the price (follower’s decision) and make their decision. The price-taking formulation is modelled as an $$N+1$$ player game with the additional player as the price-determining player. The existence of an equilibrium in such games are not easy mainly because of the coupled-constraint structure of the game and the non-convexity of the action set. We give conditions for the existence of equilibria in both formulations. We apply our results to analyze the existence of an equilibrium in the generation expansion planning problem using the above results.